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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