1. ## Simplifying square roots?

I am having a lot of trouble in my math class.
I go to school online and am stuck on a particular unit, and my book isn't doing much to helping.

I normally don't do this, but I am really at a loss and I want to graduate on time. Thanks!

7.) 3 square root of 2 - 2 square root of 3
8.) 2 square root of 3 + square root of 27 - square root of 1 / 3
9.) square root of 3 ( square root of 6 - 2 square root of 3 )
10.) square root of 1 / 2 x ( square root of 8 + square root of 2 )
11.) square root of 18 - square root of 3 / square root of 6
12.) square root of a + square root of b / square root of a - square root of b
13.) square root of 5 + 1 / square root of 5 - 1

2. 7) nothing more to do: $\displaystyle 3\sqrt{2}-2\sqrt{3}$
8) $\displaystyle 2\sqrt{3}+\sqrt{3^2\times{3}}-\sqrt{\frac{1}{3}}=2\sqrt{3}+3\sqrt{3}-\sqrt{\frac{1}{3}}$ $\displaystyle = 5\sqrt{3}-\sqrt{\frac{1}{3}} = \frac{5\times{3}-1}{\sqrt{3}}=\frac{14\sqrt{3}}{3}$
9) $\displaystyle \sqrt{3}(\sqrt{2}\times \sqrt{3}-2\sqrt{3}) = 3\sqrt{2}-6$
10) $\displaystyle \sqrt{\frac{1}{2}}(\sqrt{2^2\times 2}+\sqrt{2}) = \frac{1}{\sqrt{2}}(2\sqrt{2}+\sqrt{2}) = 3$
11) $\displaystyle \sqrt{3^2\times 2}-\frac{\sqrt{3}}{\sqrt{2}\times \sqrt{3}} = 3\sqrt{2} - \frac{\sqrt{2}}{2} = \frac{5\sqrt{2}}{2}$
12) $\displaystyle \frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}} = \frac{(\sqrt{a}+\sqrt{b})(\sqrt{a}+\sqrt{b})}{a-b} = \frac{a+b+2\sqrt{ab}}{a-b}$
13) $\displaystyle \sqrt{5}+\frac{1}{\sqrt{5}}-1 = \sqrt{5}+\frac{\sqrt{5}}{5}-1 = \frac{6\sqrt{5}}{5}-1$

3. Thank you so much, man! You are a life saver! =D