3.1 Übungen
Aus Online Mathematik Brückenkurs 1
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|width="25%" | <math>\sqrt{\sqrt{3}}</math> | |width="25%" | <math>\sqrt{\sqrt{3}}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:1| | + | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:1|Lösung a|Lösung 3.1:1a|Lösung b|Lösung 3.1:1b|Lösung c|Lösung 3.1:1c|Lösung d|Lösung 3.1:1d}} |
===Übung 3.1:2=== | ===Übung 3.1:2=== | ||
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|width="25%" | <math>\sqrt[\scriptstyle3]{-125}</math> | |width="25%" | <math>\sqrt[\scriptstyle3]{-125}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:2| | + | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:2|Lösung a|Lösung 3.1:2a|Lösung b|Lösung 3.1:2b|Lösung c|Lösung 3.1:2c|Lösung d|Lösung 3.1:2d|Lösung e|Lösung 3.1:2e|Lösung f|Lösung 3.1:2f|Lösung g|Lösung 3.1:2g}} |
===Übung 3.1:3=== | ===Übung 3.1:3=== | ||
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|width="50%" | <math>\sqrt{\displaystyle \frac{2}{3}}\bigl(\sqrt{6}-\sqrt{3}\,\bigr)</math> | |width="50%" | <math>\sqrt{\displaystyle \frac{2}{3}}\bigl(\sqrt{6}-\sqrt{3}\,\bigr)</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:3| | + | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:3|Lösung a|Lösung 3.1:3a|Lösung b|Lösung 3.1:3b|Lösung c|Lösung 3.1:3c|Lösung d|Lösung 3.1:3d}} |
===Übung 3.1:4=== | ===Übung 3.1:4=== | ||
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|width="50%" | <math>\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}</math> | |width="50%" | <math>\sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:4| | + | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:4|Lösung a|Lösung 3.1:4a|Lösung b|Lösung 3.1:4b|Lösung c|Lösung 3.1:4c|Lösung d|Lösung 3.1:4d}} |
===Übung 3.1:5=== | ===Übung 3.1:5=== | ||
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|width="25%" | <math>\displaystyle \frac{1}{\sqrt{17}-\sqrt{13}}</math> | |width="25%" | <math>\displaystyle \frac{1}{\sqrt{17}-\sqrt{13}}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:5| | + | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:5|Lösung a|Lösung 3.1:5a|Lösung b|Lösung 3.1:5b|Lösung c|Lösung 3.1:5c|Lösung d|Lösung 3.1:5d}} |
===Übung 3.1:6=== | ===Übung 3.1:6=== | ||
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|width="50%" | <math>\displaystyle \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}</math> | |width="50%" | <math>\displaystyle \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:6| | + | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:6|Lösung a|Lösung 3.1:6a|Lösung b|Lösung 3.1:6b|Lösung c|Lösung 3.1:6c|Lösung d|Lösung 3.1:6d}} |
===Übung 3.1:7=== | ===Übung 3.1:7=== | ||
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|width="33%" | <math>\displaystyle \sqrt{153}-\sqrt{68}</math> | |width="33%" | <math>\displaystyle \sqrt{153}-\sqrt{68}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:7| | + | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:7|Lösung a|Lösung 3.1:7a|Lösung b|Lösung 3.1:7b|Lösung c|Lösung 3.1:7c}} |
===Übung 3.1:8=== | ===Übung 3.1:8=== | ||
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|width="50%" | <math>\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\</math> or <math>\ \sqrt[\scriptstyle3]2\cdot3</math> | |width="50%" | <math>\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\</math> or <math>\ \sqrt[\scriptstyle3]2\cdot3</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:8| | + | </div>{{#NAVCONTENT:Antwort|Antwort 3.1:8|Lösung a|Lösung 3.1:8a|Lösung b|Lösung 3.1:8b|Lösung c|Lösung 3.1:8c|Lösung d|Lösung 3.1:8d}} |
Version vom 09:29, 22. Okt. 2008
Übung 3.1:1
Write in power form
| a) | \displaystyle \sqrt{2} | b) | \displaystyle \sqrt{7^5} | c) | \displaystyle \bigl(\sqrt[\scriptstyle3]{3}\,\bigr)^4 | d) | \displaystyle \sqrt{\sqrt{3}} |
Antwort
Laden...
Lösung a
Lösung b
Lösung c
Lösung d
Übung 3.1:2
Write in simplest possible form.
| a) | \displaystyle \sqrt{3^2} | b) | \displaystyle \sqrt{\left(-3\right)^2} | c) | \displaystyle \sqrt{-3^2} | d) | \displaystyle \sqrt{5}\cdot\sqrt[\scriptstyle3]{5}\cdot5 |
| e) | \displaystyle \sqrt{18}\cdot\sqrt{8} | f) | \displaystyle \sqrt[\scriptstyle3]{8} | g) | \displaystyle \sqrt[\scriptstyle3]{-125} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Lösung g
Übung 3.1:3
Write in simplest possible form.
| a) | \displaystyle \bigl(\sqrt{5}-\sqrt{2}\,\bigr)\bigl(\sqrt{5}+\sqrt{2}\,\bigr) | b) | \displaystyle \displaystyle \frac{\sqrt{96}}{\sqrt{18}} |
| c) | \displaystyle \sqrt{16+\sqrt{16}} | d) | \displaystyle \sqrt{\displaystyle \frac{2}{3}}\bigl(\sqrt{6}-\sqrt{3}\,\bigr) |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Übung 3.1:4
Write in simplest possible form.
| a) | \displaystyle \sqrt{0{,}16} | b) | \displaystyle \sqrt[\scriptstyle3]{0{,}027} |
| c) | \displaystyle \sqrt{50}+4\sqrt{20}-3\sqrt{18}-2\sqrt{80} | d) | \displaystyle \sqrt{48}+ \sqrt{12} +\sqrt{3} -\sqrt{75} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Übung 3.1:5
Write as an expression without a root sign in the denominator.
| a) | \displaystyle \displaystyle \frac{2}{\sqrt{12}} | b) | \displaystyle \displaystyle \frac{1}{\sqrt[\scriptstyle3]{7}} | c) | \displaystyle \displaystyle \frac{2}{3+\sqrt{7}} | d) | \displaystyle \displaystyle \frac{1}{\sqrt{17}-\sqrt{13}} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Übung 3.1:6
Write as an expression without a root sign in the denominator.
| a) | \displaystyle \displaystyle \frac{\sqrt{2}+3}{\sqrt{5}-2} | b) | \displaystyle \displaystyle \frac{1}{\left(\sqrt{3}-2\right)^2-2} |
| c) | \displaystyle \displaystyle \frac{\displaystyle \frac{1}{\sqrt{3}}-\displaystyle \frac{1}{\sqrt{5}}}{\displaystyle \frac{1}{\sqrt{2}}-\displaystyle \frac{1}{2}} | d) | \displaystyle \displaystyle \frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{6}} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Übung 3.1:7
Write in simplest possible form.
| a) | \displaystyle \displaystyle \frac{1}{\sqrt{6}-\sqrt{5}} - \displaystyle \frac{1}{\sqrt{7}-\sqrt{6}} | b) | \displaystyle \displaystyle \frac{5\sqrt{7}-7\sqrt{5}}{\sqrt{7}-\sqrt{5}} | c) | \displaystyle \displaystyle \sqrt{153}-\sqrt{68} |
Übung 3.1:8
Determine which number is the larger:
| a) | \displaystyle \sqrt[\scriptstyle3]5\ or \displaystyle \ \sqrt[\scriptstyle3]6 | b) | \displaystyle \sqrt7\ or \displaystyle \ 7 |
| c) | \displaystyle \sqrt7\ or \displaystyle \ 2{.}5 | d) | \displaystyle \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\ or \displaystyle \ \sqrt[\scriptstyle3]2\cdot3 |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
