3.1 Övningar

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(Övning 3.1:4)
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KTH.SE:u1rp004j (Diskussion | bidrag)

 
(17 mellanliggande versioner visas inte.)
Rad 1: Rad 1:
 +
==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&nbsp;</div> <div class=NavHead>Facit&nbsp;</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>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</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:
F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt
<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&nbsp;</div> <div class=NavHead>Facit&nbsp;</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>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</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>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</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>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</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>L&ouml;sning g&nbsp;</div>+<div class=NavHead>L&ouml;sning g)&nbsp;</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:
F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt
<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&nbsp;</div> <div class=NavHead>Facit&nbsp;</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>L&ouml;sning &nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga <br \>[[Bild:]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_3a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +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 class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_3c.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning d)&nbsp;</div>
 +<div class=NavContent>
 +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 234: Rad 368:
F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
 +
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="50%">$\sqrt{0{,}16}$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="50%">$\sqrt[\scriptstyle3]{0{,}027}$</td>
 +</tr>
 +
 +<tr align="left">
 +<td class="ntext">c)</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" width="50%">$\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}$</td>
 +<td class="ntext"></td>
 +</tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
 +</table>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>Facit&nbsp;</div>
 +<div class=NavContent>
 +Facit till alla delfrågor<br \>
 +<table width="100%" cellspacing="10px">
 +
<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%">$0{,}4$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$\sqrt[\scriptstyle3]{0,027}$</td>+<td class="ntext" width="50%">$0{,}3$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)</td>
 +<td class="ntext" width="50%">$-4\sqrt{2}$</td>
 +<td class="ntext">d)</td>
 +<td class="ntext" width="50%">$2\sqrt{3}$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_4a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_4b.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_4c.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning d)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_4d.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +==&Ouml;vning 3.1:5==
 +
 +<div class="ovning">
 +Skriv som ett uttryck utan rottecken i n&auml;mnaren.
 +<table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{2}{\sqrt{12}}$</td>
 +<td class="ntext">b)</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">$\sqrt{50}+4\sqrt{20}-3\sqrt{18}-2\sqrt{80}$</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">$\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}$</td>+<td class="ntext" width="25%">$\displaystyle \frac{1}{\sqrt{17}-\sqrt{13}}$</td>
-<td class="ntext"></td>+
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 256: Rad 488:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</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">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{\sqrt{3}}{3}$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{7^{2/3}}{7}$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="25%">$3-\sqrt{7}$</td>
 +<td class="ntext">d)</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4}$</td>
 +</tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_5a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_5b.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_5c.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning d)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_5d.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +==&Ouml;vning 3.1:6==
 +
 +<div class="ovning">
 +Skriv som ett uttryck utan rottecken i n&auml;mnaren.
 +<table width="100%" cellspacing="10px">
<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%">$\displaystyle \frac{\sqrt{2}+3}{\sqrt{5}-2}$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$0,3$</td>+<td class="ntext" width="50%">$\displaystyle \frac{1}{\left(\sqrt{3}-2\right)^2-2}$</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%">$\displaystyle \frac{\displaystyle \frac{1}{\sqrt{3}}-\displaystyle \frac{1}{\sqrt{5}}}{\displaystyle \frac{1}{\sqrt{2}}-\displaystyle \frac{1}{2}}$</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$2\sqrt{3}$</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>
 +</table>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>Facit&nbsp;</div>
 +<div class=NavContent>
 +Facit till alla delfrågor<br \>
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="50%">$6+2\sqrt{2}+3\sqrt{5}+\sqrt{10}$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="50%">$-\displaystyle \frac{5+4\sqrt{3}}{23}$</td>
 +</tr>
 +
 +<tr align="left">
 +<td class="ntext">c)</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" width="50%">$\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23}$</td>
 +</tr>
 +<tr><td height="5px"/></tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_6a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_6b.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +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 class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning d)&nbsp;</div>
 +<div class=NavContent>
 +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>
 +
 +==&Ouml;vning 3.1:7==
 +
 +<div class="ovning">
 +F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt
 +<table width="100%" cellspacing="10px">
 +
 +<tr align="left">
 +<td class="ntext">a)</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" width="33%">$\displaystyle \frac{5\sqrt{7}-7\sqrt{5}}{\sqrt{7}-\sqrt{5}}$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$\displaystyle \sqrt{153}-\sqrt{68}$</td>
 +</tr>
 +<tr><td height="5px"/></tr>
 +</table>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>Facit&nbsp;</div>
 +<div class=NavContent>
 +Facit till alla delfrågor<br \>
 +<table width="100%" cellspacing="10px">
 +
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="33%">$\sqrt{5}-\sqrt{7}$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="33%">$-\sqrt{35}$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$\sqrt{17}$</td>
 +</tr>
 +<tr><td height="5px"/></tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_7a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_7b.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_7c.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +==&Ouml;vning 3.1:8==
 +
 +<div class="ovning">
 +Avg&ouml;r vilket tal som &auml;r st&ouml;rst av
 +<table width="100%" cellspacing="10px">
 +
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="50%">$\sqrt[\scriptstyle3]5\ $ och $\ \sqrt[\scriptstyle3]6$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="50%">$\sqrt7\ $ och $\ 7$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)</td>
 +<td class="ntext" width="50%">$\sqrt7\ $ och $\ 2{,}5$</td>
 +<td class="ntext">d)</td>
 +<td class="ntext" width="50%">$\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ $ och $\ \sqrt[\scriptstyle3]2\cdot3$</td>
 +</tr>
 +<tr><td height="5px"/></tr>
 +</table>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>Facit&nbsp;</div>
 +<div class=NavContent>
 +Facit till alla delfrågor<br \>
 +<table width="100%" cellspacing="10px">
 +
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="50%">$\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="50%">$7 > \sqrt7$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)</td>
 +<td class="ntext" width="50%">$\sqrt7 > 2{,}5$</td>
 +<td class="ntext">d)</td>
 +<td class="ntext" width="50%">$\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3$</td>
 +</tr>
 +<tr><td height="5px"/></tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_8a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_8b.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:3_1_8c.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning d)&nbsp;</div>
 +<div class=NavContent>
 +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> </table>
</div> </div>
</div> </div>

Nuvarande version

Innehåll

[redigera] Övning 3.1:1

Skriv i potensform

a) $\sqrt{2}$ b) $\sqrt{7^5}$ c) $\bigl(\sqrt[\scriptstyle3]{3}\,\bigr)^4$ d) $\sqrt{\sqrt{3}}$

[redigera] 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) $\sqrt[\scriptstyle3]{-125}$

[redigera] 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) $\sqrt{\displaystyle \frac{2}{3}}\bigl(\sqrt{6}-\sqrt{3}\,\bigr)$

[redigera] 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) $\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}$

[redigera] 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) $\displaystyle \frac{1}{\sqrt{17}-\sqrt{13}}$




[redigera] 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) $\displaystyle \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}$

[redigera] 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) $\displaystyle \sqrt{153}-\sqrt{68}$

[redigera] 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 $\ \sqrt[\scriptstyle3]2\cdot3$
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