3.1 Exercises
From Förberedande kurs i matematik 1
| Theory | Exercises |
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}} |
Answer
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Solution a
Solution b
Solution c
Solution 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} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Solution 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) |
Answer
Solution a
Solution b
Solution c
Solution 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} |
Answer
Solution a
Solution b
Solution c
Solution 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}} |
Answer
Solution a
Solution b
Solution c
Solution 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}} |
Answer
Solution a
Solution b
Solution c
Solution 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} |
Answer
Solution a
Solution b
Solution c
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 |
Answer
Solution a
Solution b
Solution c
Solution d
