3.1 Übungen
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
K (Regenerate images and tabs) |
|||
| Zeile 2: | Zeile 2: | ||
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | ||
| style="border-bottom:1px solid #000" width="5px" | | | style="border-bottom:1px solid #000" width="5px" | | ||
| - | {{Ej vald flik|[[3.1 Rötter| | + | {{Ej vald flik|[[3.1 Rötter|Theoty]]}} |
| - | {{Vald flik|[[3.1 Övningar| | + | {{Vald flik|[[3.1 Övningar|Exercises]]}} |
| style="border-bottom:1px solid #000" width="100%"| | | style="border-bottom:1px solid #000" width="100%"| | ||
|} | |} | ||
| - | === | + | ===Exercise 3.1:1=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Write in power form | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 23: | Zeile 23: | ||
</div>{{#NAVCONTENT:Svar|Svar 3.1:1|Lösning a|Lösning 3.1:1a|Lösning b|Lösning 3.1:1b|Lösning c|Lösning 3.1:1c|Lösning d|Lösning 3.1:1d}} | </div>{{#NAVCONTENT:Svar|Svar 3.1:1|Lösning a|Lösning 3.1:1a|Lösning b|Lösning 3.1:1b|Lösning c|Lösning 3.1:1c|Lösning d|Lösning 3.1:1d}} | ||
| - | === | + | ===Exercise 3.1:2=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Write in simplest possible form. | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 45: | Zeile 45: | ||
</div>{{#NAVCONTENT:Svar|Svar 3.1:2|Lösning a|Lösning 3.1:2a|Lösning b|Lösning 3.1:2b|Lösning c|Lösning 3.1:2c|Lösning d|Lösning 3.1:2d|Lösning e|Lösning 3.1:2e|Lösning f|Lösning 3.1:2f|Lösning g|Lösning 3.1:2g}} | </div>{{#NAVCONTENT:Svar|Svar 3.1:2|Lösning a|Lösning 3.1:2a|Lösning b|Lösning 3.1:2b|Lösning c|Lösning 3.1:2c|Lösning d|Lösning 3.1:2d|Lösning e|Lösning 3.1:2e|Lösning f|Lösning 3.1:2f|Lösning g|Lösning 3.1:2g}} | ||
| - | === | + | ===Exercise 3.1:3=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Write in simplest possible form. | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 61: | Zeile 61: | ||
</div>{{#NAVCONTENT:Svar|Svar 3.1:3|Lösning a|Lösning 3.1:3a|Lösning b|Lösning 3.1:3b|Lösning c|Lösning 3.1:3c|Lösning d|Lösning 3.1:3d}} | </div>{{#NAVCONTENT:Svar|Svar 3.1:3|Lösning a|Lösning 3.1:3a|Lösning b|Lösning 3.1:3b|Lösning c|Lösning 3.1:3c|Lösning d|Lösning 3.1:3d}} | ||
| - | === | + | ===Exercise 3.1:4=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Write in simplest possible form. | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 77: | Zeile 77: | ||
</div>{{#NAVCONTENT:Svar|Svar 3.1:4|Lösning a|Lösning 3.1:4a|Lösning b|Lösning 3.1:4b|Lösning c|Lösning 3.1:4c|Lösning d|Lösning 3.1:4d}} | </div>{{#NAVCONTENT:Svar|Svar 3.1:4|Lösning a|Lösning 3.1:4a|Lösning b|Lösning 3.1:4b|Lösning c|Lösning 3.1:4c|Lösning d|Lösning 3.1:4d}} | ||
| - | === | + | ===Exercise 3.1:5=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Write as an expression without a root sign in the denominator. | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 92: | Zeile 92: | ||
</div>{{#NAVCONTENT:Svar|Svar 3.1:5|Lösning a|Lösning 3.1:5a|Lösning b|Lösning 3.1:5b|Lösning c|Lösning 3.1:5c|Lösning d|Lösning 3.1:5d}} | </div>{{#NAVCONTENT:Svar|Svar 3.1:5|Lösning a|Lösning 3.1:5a|Lösning b|Lösning 3.1:5b|Lösning c|Lösning 3.1:5c|Lösning d|Lösning 3.1:5d}} | ||
| - | === | + | ===Exercise 3.1:6=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Write as an expression without a root sign in the denominator. | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 108: | Zeile 108: | ||
</div>{{#NAVCONTENT:Svar|Svar 3.1:6|Lösning a|Lösning 3.1:6a|Lösning b|Lösning 3.1:6b|Lösning c|Lösning 3.1:6c|Lösning d|Lösning 3.1:6d}} | </div>{{#NAVCONTENT:Svar|Svar 3.1:6|Lösning a|Lösning 3.1:6a|Lösning b|Lösning 3.1:6b|Lösning c|Lösning 3.1:6c|Lösning d|Lösning 3.1:6d}} | ||
| - | === | + | ===Exercise 3.1:7=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Write in simplest possible form. | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 121: | Zeile 121: | ||
</div>{{#NAVCONTENT:Svar|Svar 3.1:7|Lösning a|Lösning 3.1:7a|Lösning b|Lösning 3.1:7b|Lösning c|Lösning 3.1:7c}} | </div>{{#NAVCONTENT:Svar|Svar 3.1:7|Lösning a|Lösning 3.1:7a|Lösning b|Lösning 3.1:7b|Lösning c|Lösning 3.1:7c}} | ||
| - | === | + | ===Exercise 3.1:8=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Determine which number is the larger: | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="50%" | <math>\sqrt[\scriptstyle3]5\ </math> | + | |width="50%" | <math>\sqrt[\scriptstyle3]5\ </math> or <math>\ \sqrt[\scriptstyle3]6</math> |
|b) | |b) | ||
| - | |width="50%" | <math>\sqrt7\ </math> | + | |width="50%" | <math>\sqrt7\ </math> or <math>\ 7</math> |
|- | |- | ||
|c) | |c) | ||
| - | |width="50%" | <math>\sqrt7\ </math> | + | |width="50%" | <math>\sqrt7\ </math> or <math>\ 2{.}5</math> |
|d) | |d) | ||
| - | |width="50%" | <math>\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\</math> | + | |width="50%" | <math>\sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3\</math> or <math>\ \sqrt[\scriptstyle3]2\cdot3</math> |
|} | |} | ||
</div>{{#NAVCONTENT:Svar|Svar 3.1:8|Lösning a|Lösning 3.1:8a|Lösning b|Lösning 3.1:8b|Lösning c|Lösning 3.1:8c|Lösning d|Lösning 3.1:8d}} | </div>{{#NAVCONTENT:Svar|Svar 3.1:8|Lösning a|Lösning 3.1:8a|Lösning b|Lösning 3.1:8b|Lösning c|Lösning 3.1:8c|Lösning d|Lösning 3.1:8d}} | ||
Version vom 13:49, 3. Aug. 2008
Exercise 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}} |
Svar
Laden...
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
Lösning g
Exercise 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) |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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}} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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}} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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} |
Exercise 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 |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
