# How do you simplify 6/sqrt20?

Jan 29, 2016

$\frac{6}{\sqrt{5}} = \frac{3}{5} \sqrt{5}$

#### Explanation:

$\frac{6}{\sqrt{20}}$
$\textcolor{w h i t e}{\text{XXX}} = \frac{6}{\sqrt{{2}^{2} \times 5}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{6}{2} \sqrt{5}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{3}{\sqrt{5}}$

Often when asked to simplify a fraction containing a radical, we are expected to clear the radical from the denominator;
so...
$\textcolor{w h i t e}{\text{XXX}} = \frac{3}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{3 \sqrt{5}}{5}$