# How do you simplify square roots? (examples of problems I need help with down below in the description)

## Simplify, 1) $\sqrt{20}$ 2) $\frac{12}{\sqrt{3}}$ 3) $\frac{\sqrt{6}}{12}$

Oct 2, 2017

1) $2 \sqrt{5}$
2) $4 \sqrt{3}$
3) $\frac{1}{2 \sqrt{6}}$

#### Explanation:

1) $\sqrt{20} = \sqrt{5 \cdot 2 \cdot 2} = \sqrt{5 \cdot {2}^{2}} = 2 \sqrt{5}$
2) $\frac{12}{\sqrt{3}} = \frac{3 \cdot 4}{\sqrt{3}} = \sqrt{3} \cdot \textcolor{red}{\cancel{\sqrt{3}}} \cdot \frac{4}{\textcolor{red}{\cancel{\sqrt{3}}}} = 4 \cdot \sqrt{3}$
3) $\frac{\sqrt{6}}{12} = \frac{\textcolor{red}{\cancel{\sqrt{6}}}}{2 \cdot \sqrt{6} \cdot \textcolor{red}{\cancel{\sqrt{6}}}}$
$= \frac{1}{2 \sqrt{6}}$