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Övningar 3.1 - Versionshistorik
2026-05-16T16:45:04Z
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KTH.SE:u1zpa8nw den 17 juli 2007 kl. 09.41
2007-07-17T09:41:42Z
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KTH.SE:u1zpa8nw den 16 juli 2007 kl. 11.07
2007-07-16T11:07:53Z
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KTH.SE:u1zpa8nw
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KTH.SE:u1zpa8nw: Ny sida: __NOTOC__ ==Övning 3.1:1== <div class="ovning"> Skriv i potensform <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="25%">$\s...
2007-07-16T08:07:43Z
<p>Ny sida: __NOTOC__ ==&Ouml;vning 3.1:1== <div class="ovning"> Skriv i potensform <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="25%">$\s...</p>
<p><b>Ny sida</b></p><div>__NOTOC__<br />
==&Ouml;vning 3.1:1==<br />
<div class="ovning"><br />
Skriv i potensform<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$\sqrt{2}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$\sqrt{7^5}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$\bigl(\sqrt[\scriptstyle3]{3}\,\bigr)^4$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$\sqrt{\sqrt{3}}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 3.1:2==<br />
<div class="ovning"><br />
F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$\sqrt{3^2}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$\sqrt{\left(-3\right)^2}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$\sqrt{-3^2}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$\sqrt{5}\cdot\sqrt[\scriptstyle3]{5}\cdot5$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="25%">$\sqrt{18}\cdot\sqrt{8}$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="25%">$\sqrt[\scriptstyle3]{8}$</td> <br />
<td class="ntext">g)</td><br />
<td class="ntext" width="25%">$\sqrt[\scriptstyle3]{-125}$</td><br />
<td></td><br />
<td></td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 3.1:3==<br />
<div class="ovning"><br />
F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\bigl(\sqrt{5}-\sqrt{2}\,\bigr)\bigl(\sqrt{5}+\sqrt{2}\,\bigr)$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{\sqrt{96}}{\sqrt{18}}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\sqrt{16+\sqrt{16}}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\sqrt{\displaystyle \frac{2}{3}}\bigl(\sqrt{6}-\sqrt{3}\,\bigr)$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 3.1:4==<br />
<div class="ovning"><br />
F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\sqrt{0{,}16}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\sqrt[\scriptstyle3]{0{,}027}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\sqrt{50}+4\sqrt{20}-3\sqrt{18}-2\sqrt{80}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}$</td><br />
<td class="ntext"></td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 3.1:5==<br />
<div class="ovning"><br />
Skriv som ett uttryck utan rottecken i n&auml;mnaren.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$\displaystyle \frac{2}{\sqrt{12}}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$\displaystyle \frac{1}{\sqrt[\scriptstyle3]{7}}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$\displaystyle \frac{2}{3+\sqrt{7}}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$\displaystyle \frac{1}{\sqrt{17}-\sqrt{13}}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 3.1:6==<br />
<div class="ovning"><br />
Skriv som ett uttryck utan rottecken i n&auml;mnaren.<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{\sqrt{2}+3}{\sqrt{5}-2}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{\left(\sqrt{3}-2\right)^2-2}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<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><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 3.1:7==<br />
<div class="ovning"><br />
F&ouml;renkla s&aring; l&aring;ngt som m&ouml;jligt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{1}{\sqrt{6}-\sqrt{5}} - \displaystyle \frac{1}{\sqrt{7}-\sqrt{6}}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{5\sqrt{7}-7\sqrt{5}}{\sqrt{7}-\sqrt{5}}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle \sqrt{153}-\sqrt{68}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 3.1:8==<br />
<div class="ovning"><br />
Avg&ouml;r vilket tal som &auml;r st&ouml;rst av<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\sqrt[\scriptstyle3]5\ $ och $\ \sqrt[\scriptstyle3]6$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\sqrt7\ $ och $\ 7$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\sqrt7\ $ och $\ 2{,}5$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ $ och $\ \sqrt[\scriptstyle3]2\cdot3$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div></div>
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