3.1 Exercises

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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}}

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}

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)

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}

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}}

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}}

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