3.1 Övningar
Sommarmatte 1
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| Rad 1: | Rad 1: | ||
| + | __NOTOC__ | ||
| ==Övning 3.1:1== | ==Övning 3.1:1== | ||
| Rad 4: | Rad 5: | ||
| Skriv i potensform | Skriv i potensform | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\sqrt{2}$</td> | + | <td class="ntext" width="25%">$\sqrt{2}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\sqrt{7^5}$</td> | + | <td class="ntext" width="25%">$\sqrt{7^5}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\left(\sqrt[\scriptstyle3]{3}\right)^4$</td> | + | <td class="ntext" width="25%">$\bigl(\sqrt[\scriptstyle3]{3}\,\bigr)^4$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\sqrt{\sqrt{3}}$</td> | + | <td class="ntext" width="25%">$\sqrt{\sqrt{3}}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 22: | Rad 22: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$2^{1/2}$</td> | + | <td class="ntext" width="25%">$2^{1/2}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$7^{5/2}$</td> | + | <td class="ntext" width="25%">$7^{5/2}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$3^{4/3}$</td> | + | <td class="ntext" width="25%">$3^{4/3}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$3^{1/4}$</td> | + | <td class="ntext" width="25%">$3^{1/4}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 41: | Rad 40: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_1_1a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_1a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_1_1b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_1b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_1_1c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_1c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_1_1d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_1d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 73: | Rad 100: | ||
| Förenkla så långt som möjligt | Förenkla så långt som möjligt | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\sqrt{3^2}$</td> | + | <td class="ntext" width="25%">$\sqrt{3^2}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\sqrt{\left(-3\right)^2}$</td> | + | <td class="ntext" width="25%">$\sqrt{\left(-3\right)^2}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\sqrt{-3^2}$</td> | + | <td class="ntext" width="25%">$\sqrt{-3^2}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\sqrt{5}\cdot\sqrt[\scriptstyle3]{5}\cdot5$</td> | + | <td class="ntext" width="25%">$\sqrt{5}\cdot\sqrt[\scriptstyle3]{5}\cdot5$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">$\sqrt{18}\cdot\sqrt{8}$</td> | + | <td class="ntext" width="25%">$\sqrt{18}\cdot\sqrt{8}$</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">$\sqrt[\scriptstyle3]{8}$</td> | + | <td class="ntext" width="25%">$\sqrt[\scriptstyle3]{8}$</td> |
| <td class="ntext">g)</td> | <td class="ntext">g)</td> | ||
| - | <td class="ntext">$\sqrt[\scriptstyle3]{-125}$</td> | + | <td class="ntext" width="25%">$\sqrt[\scriptstyle3]{-125}$</td> |
| <td></td> | <td></td> | ||
| <td></td> | <td></td> | ||
| Rad 102: | Rad 129: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$3$</td> | + | <td class="ntext" width="25%">$3$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$3$</td> | + | <td class="ntext" width="25%">$3$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">ej def.*</td> | + | <td class="ntext" width="25%">ej definierad</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$5^{11/6}$</td> | + | <td class="ntext" width="25%">$5^{11/6}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">$12$</td> | + | <td class="ntext" width="25%">$12$</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">$2$</td> | + | <td class="ntext" width="25%">$2$</td> |
| <td class="ntext">g)</td> | <td class="ntext">g)</td> | ||
| - | <td class="ntext">$-5$</td> | + | <td class="ntext" width="25%">$-5$</td> |
| <td></td> | <td></td> | ||
| <td></td> | <td></td> | ||
| Rad 133: | Rad 160: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_1_2a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_2a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_1_2b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_2b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_1_2c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_2c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_1_2d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_2d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e<br \>[[Bild:3_1_2e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_2e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning f </div> | + | <div class=NavHead>Lösning f) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga f<br \>[[Bild:3_1_2f.gif]] | + | Lösning till delfråga f) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_2f.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning g </div> | + | <div class=NavHead>Lösning g) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga g<br \>[[Bild:3_1_2g.gif]] | + | Lösning till delfråga g) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_2g.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 186: | Rad 262: | ||
| Förenkla så långt som möjligt | Förenkla så långt som möjligt | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)$</td> | + | <td class="ntext" width="50%">$\bigl(\sqrt{5}-\sqrt{2}\,\bigr)\bigl(\sqrt{5}+\sqrt{2}\,\bigr)$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{\sqrt{96}}{\sqrt{18}}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{\sqrt{96}}{\sqrt{18}}$</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\sqrt{16+\sqrt{16}}$</td> | + | <td class="ntext" width="50%">$\sqrt{16+\sqrt{16}}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\sqrt{\displaystyle \frac{2}{3}}\left(\sqrt{6}-\sqrt{3}\right)$</td> | + | <td class="ntext" width="50%">$\sqrt{\displaystyle \frac{2}{3}}\bigl(\sqrt{6}-\sqrt{3}\,\bigr)$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 204: | Rad 282: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$3$</td> | + | <td class="ntext" width="50%">$3$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{4\sqrt{3}}{3}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{4\sqrt{3}}{3}$</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$2\sqrt{5}$</td> | + | <td class="ntext" width="50%">$2\sqrt{5}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$2-\sqrt{2}$</td> | + | <td class="ntext" width="50%">$2-\sqrt{2}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 223: | Rad 303: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_1_3a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_3a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_1_3b-1(2).gif]]<br \>[[Bild:3_1_3b-2(2).gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_3b-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_3b-2(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_1_3c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_3c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_1_3d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_3d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 255: | Rad 368: | ||
| Förenkla så långt som möjligt | Förenkla så långt som möjligt | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\sqrt{0,16}$</td> | + | <td class="ntext" width="50%">$\sqrt{0{,}16}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\sqrt[\scriptstyle3]{0,027}$</td> | + | <td class="ntext" width="50%">$\sqrt[\scriptstyle3]{0{,}027}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\sqrt{50}+4\sqrt{20}-3\sqrt{18}-2\sqrt{80}$</td> | + | <td class="ntext" width="50%">$\sqrt{50}+4\sqrt{20}-3\sqrt{18}-2\sqrt{80}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}$</td> | + | <td class="ntext" width="50%">$\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}$</td> |
| <td class="ntext"></td> | <td class="ntext"></td> | ||
| </tr> | </tr> | ||
| Rad 277: | Rad 390: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$0,4$</td> | + | <td class="ntext" width="50%">$0{,}4$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$0,3$</td> | + | <td class="ntext" width="50%">$0{,}3$</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$-4\sqrt{2}$</td> | + | <td class="ntext" width="50%">$-4\sqrt{2}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$2\sqrt{3}$</td> | + | <td class="ntext" width="50%">$2\sqrt{3}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 296: | Rad 411: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_1_4a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_4a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_1_4b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_4b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_1_4c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_4c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_1_4d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_4d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 330: | Rad 473: | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{2}{\sqrt{12}}$</td> | + | <td class="ntext" width="25%">$\displaystyle \frac{2}{\sqrt{12}}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{1}{\sqrt[\scriptstyle3]{7}}$</td> | + | <td class="ntext" width="25%">$\displaystyle \frac{1}{\sqrt[\scriptstyle3]{7}}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{2}{3+\sqrt{7}}$</td> | + | <td class="ntext" width="25%">$\displaystyle \frac{2}{3+\sqrt{7}}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{1}{\sqrt{17}-\sqrt{13}}$</td> | + | <td class="ntext" width="25%">$\displaystyle \frac{1}{\sqrt{17}-\sqrt{13}}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 345: | Rad 488: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{\sqrt{3}}{3}$</td> | + | <td class="ntext" width="25%">$\displaystyle \frac{\sqrt{3}}{3}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{7^{2/3}}{7}$</td> | + | <td class="ntext" width="25%">$\displaystyle \frac{7^{2/3}}{7}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$3-\sqrt{7}$</td> | + | <td class="ntext" width="25%">$3-\sqrt{7}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4}$</td> | + | <td class="ntext" width="25%">$\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 363: | Rad 506: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_1_5a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_5a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 371: | Rad 521: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_1_5b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_5b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 379: | Rad 536: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_1_5c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_5c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 387: | Rad 551: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_1_5d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_5d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 400: | Rad 571: | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{\sqrt{2}+3}{\sqrt{5}-2}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{\sqrt{2}+3}{\sqrt{5}-2}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{1}{\left(\sqrt{3}-2\right)^2-2}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{1}{\left(\sqrt{3}-2\right)^2-2}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{\displaystyle \frac{1}{\sqrt{3}}-\displaystyle \frac{1}{\sqrt{5}}}{\displaystyle \frac{1}{\sqrt{2}}-\displaystyle \frac{1}{2}}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{\displaystyle \frac{1}{\sqrt{3}}-\displaystyle \frac{1}{\sqrt{5}}}{\displaystyle \frac{1}{\sqrt{2}}-\displaystyle \frac{1}{2}}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 418: | Rad 589: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$6+2\sqrt{2}+3\sqrt{5}+\sqrt{10}$</td> | + | <td class="ntext" width="50%">$6+2\sqrt{2}+3\sqrt{5}+\sqrt{10}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$-\displaystyle \frac{5+4\sqrt{3}}{23}$</td> | + | <td class="ntext" width="50%">$-\displaystyle \frac{5+4\sqrt{3}}{23}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{2}{3}\sqrt{6}+\displaystyle \frac{2}{3}\sqrt{3}-\displaystyle \frac{2}{5}\sqrt{10}-\displaystyle \frac{2}{5}\sqrt{5}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{2}{3}\sqrt{6}+\displaystyle \frac{2}{3}\sqrt{3}-\displaystyle \frac{2}{5}\sqrt{10}-\displaystyle \frac{2}{5}\sqrt{5}$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 439: | Rad 610: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_1_6a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_6a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_1_6b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_6b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_1_6c-1(2).gif]]<br \>[[Bild:3_1_6c-2(2).gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_6c-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_6c-2(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_1_6d-1(2).gif]]<br \>[[Bild:3_1_6d-2(2).gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_6d-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_6d-2(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 471: | Rad 680: | ||
| Förenkla så långt som möjligt | Förenkla så långt som möjligt | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{1}{\sqrt{6}-\sqrt{5}} - \displaystyle \frac{1}{\sqrt{7}-\sqrt{6}}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{1}{\sqrt{6}-\sqrt{5}} - \displaystyle \frac{1}{\sqrt{7}-\sqrt{6}}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{5\sqrt{7}-7\sqrt{5}}{\sqrt{7}-\sqrt{5}}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{5\sqrt{7}-7\sqrt{5}}{\sqrt{7}-\sqrt{5}}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\displaystyle \sqrt{153}-\sqrt{68}$</td> | + | <td class="ntext" width="33%">$\displaystyle \sqrt{153}-\sqrt{68}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 487: | Rad 696: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\sqrt{5}-\sqrt{7}$</td> | + | <td class="ntext" width="33%">$\sqrt{5}-\sqrt{7}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$-\sqrt{35}$</td> | + | <td class="ntext" width="33%">$-\sqrt{35}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\sqrt{17}$</td> | + | <td class="ntext" width="33%">$\sqrt{17}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 504: | Rad 713: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_1_7a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_7a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_1_7b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_7b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_1_7c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_7c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 529: | Rad 759: | ||
| Avgör vilket tal som är störst av | Avgör vilket tal som är störst av | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\sqrt[\scriptstyle3]5$ och $\sqrt[\scriptstyle3]6$</td> | + | <td class="ntext" width="50%">$\sqrt[\scriptstyle3]5\ $ och $\ \sqrt[\scriptstyle3]6$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\sqrt7$ och $7$</td> | + | <td class="ntext" width="50%">$\sqrt7\ $ och $\ 7$</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\sqrt7$ och $2,5$</td> | + | <td class="ntext" width="50%">$\sqrt7\ $ och $\ 2{,}5$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\sqrt2\left(\sqrt[\scriptstyle4]3\right)^3$ och $\sqrt[\scriptstyle3]2\cdot3$</td> | + | <td class="ntext" width="50%">$\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ $ och $\ \sqrt[\scriptstyle3]2\cdot3$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 547: | Rad 779: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5$</td> | + | <td class="ntext" width="50%">$\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$7 > \sqrt7$</td> | + | <td class="ntext" width="50%">$7 > \sqrt7$</td> |
| + | </tr> | ||
| + | <tr align="left"> | ||
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\sqrt7 > 2,5$</td> | + | <td class="ntext" width="50%">$\sqrt7 > 2{,}5$</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\left(\sqrt[\scriptstyle4]3\right)^3$</td> | + | <td class="ntext" width="50%">$\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 566: | Rad 800: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:3_1_8a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_8a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:3_1_8b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_8b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:3_1_8c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_8c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:3_1_8d-1(2).gif]]<br \>[[Bild:3_1_8d-2(2).gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_8d-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:3_1_8d-2(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
Versionen från 14 maj 2007 kl. 08.19
Övning 3.1:1
Skriv i potensform
| a) | $\sqrt{2}$ | b) | $\sqrt{7^5}$ | c) | $\bigl(\sqrt[\scriptstyle3]{3}\,\bigr)^4$ | d) | $\sqrt{\sqrt{3}}$ |
Facit
Facit till alla delfrågor
| a) | $2^{1/2}$ | b) | $7^{5/2}$ | c) | $3^{4/3}$ | d) | $3^{1/4}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Övning 3.1:2
Förenkla så långt som möjligt
| a) | $\sqrt{3^2}$ | b) | $\sqrt{\left(-3\right)^2}$ | c) | $\sqrt{-3^2}$ | d) | $\sqrt{5}\cdot\sqrt[\scriptstyle3]{5}\cdot5$ |
| e) | $\sqrt{18}\cdot\sqrt{8}$ | f) | $\sqrt[\scriptstyle3]{8}$ | g) | $\sqrt[\scriptstyle3]{-125}$ | ||
Facit
Facit till alla delfrågor
| a) | $3$ | b) | $3$ | c) | ej definierad | d) | $5^{11/6}$ |
| e) | $12$ | f) | $2$ | g) | $-5$ | ||
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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Lösning f)
Lösning till delfråga f)
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Lösning g)
Lösning till delfråga g)
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Övning 3.1:3
Förenkla så långt som möjligt
| a) | $\bigl(\sqrt{5}-\sqrt{2}\,\bigr)\bigl(\sqrt{5}+\sqrt{2}\,\bigr)$ | b) | $\displaystyle \frac{\sqrt{96}}{\sqrt{18}}$ |
| c) | $\sqrt{16+\sqrt{16}}$ | d) | $\sqrt{\displaystyle \frac{2}{3}}\bigl(\sqrt{6}-\sqrt{3}\,\bigr)$ |
Facit
Facit till alla delfrågor
| a) | $3$ | b) | $\displaystyle \frac{4\sqrt{3}}{3}$ |
| c) | $2\sqrt{5}$ | d) | $2-\sqrt{2}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Övning 3.1:4
Förenkla så långt som möjligt
| a) | $\sqrt{0{,}16}$ | b) | $\sqrt[\scriptstyle3]{0{,}027}$ | |
| c) | $\sqrt{50}+4\sqrt{20}-3\sqrt{18}-2\sqrt{80}$ | d) | $\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}$ | |
Facit
Facit till alla delfrågor
| a) | $0{,}4$ | b) | $0{,}3$ |
| c) | $-4\sqrt{2}$ | d) | $2\sqrt{3}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Övning 3.1:5
Skriv som ett uttryck utan rottecken i nämnaren.
| a) | $\displaystyle \frac{2}{\sqrt{12}}$ | b) | $\displaystyle \frac{1}{\sqrt[\scriptstyle3]{7}}$ | c) | $\displaystyle \frac{2}{3+\sqrt{7}}$ | d) | $\displaystyle \frac{1}{\sqrt{17}-\sqrt{13}}$ |
Facit
Facit till alla delfrågor
| a) | $\displaystyle \frac{\sqrt{3}}{3}$ | b) | $\displaystyle \frac{7^{2/3}}{7}$ | c) | $3-\sqrt{7}$ | d) | $\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Övning 3.1:6
Skriv som ett uttryck utan rottecken i nämnaren.
| a) | $\displaystyle \frac{\sqrt{2}+3}{\sqrt{5}-2}$ | b) | $\displaystyle \frac{1}{\left(\sqrt{3}-2\right)^2-2}$ |
| c) | $\displaystyle \frac{\displaystyle \frac{1}{\sqrt{3}}-\displaystyle \frac{1}{\sqrt{5}}}{\displaystyle \frac{1}{\sqrt{2}}-\displaystyle \frac{1}{2}}$ | d) | $\displaystyle \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}$ |
Facit
Facit till alla delfrågor
| a) | $6+2\sqrt{2}+3\sqrt{5}+\sqrt{10}$ | b) | $-\displaystyle \frac{5+4\sqrt{3}}{23}$ |
| c) | $\displaystyle \frac{2}{3}\sqrt{6}+\displaystyle \frac{2}{3}\sqrt{3}-\displaystyle \frac{2}{5}\sqrt{10}-\displaystyle \frac{2}{5}\sqrt{5}$ | d) | $\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Övning 3.1:7
Förenkla så långt som möjligt
| a) | $\displaystyle \frac{1}{\sqrt{6}-\sqrt{5}} - \displaystyle \frac{1}{\sqrt{7}-\sqrt{6}}$ | b) | $\displaystyle \frac{5\sqrt{7}-7\sqrt{5}}{\sqrt{7}-\sqrt{5}}$ | c) | $\displaystyle \sqrt{153}-\sqrt{68}$ |
Facit
Facit till alla delfrågor
| a) | $\sqrt{5}-\sqrt{7}$ | b) | $-\sqrt{35}$ | c) | $\sqrt{17}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Övning 3.1:8
Avgör vilket tal som är störst av
| a) | $\sqrt[\scriptstyle3]5\ $ och $\ \sqrt[\scriptstyle3]6$ | b) | $\sqrt7\ $ och $\ 7$ |
| c) | $\sqrt7\ $ och $\ 2{,}5$ | d) | $\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ $ och $\ \sqrt[\scriptstyle3]2\cdot3$ |
Facit
Facit till alla delfrågor
| a) | $\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5$ | b) | $7 > \sqrt7$ |
| c) | $\sqrt7 > 2{,}5$ | d) | $\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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