# How do you simplify sqrt(400/5)?

Mar 15, 2018

See below.

#### Explanation:

$\sqrt{\frac{400}{5}} = \frac{\sqrt{400}}{\sqrt{5}}$

$\frac{\sqrt{400}}{\sqrt{5}} = \frac{20}{\sqrt{5}}$

$= \frac{20}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

$= \frac{20 \sqrt{5}}{5} = 4 \sqrt{5}$

Mar 15, 2018

$\sqrt{\frac{400}{5}} = 4 \sqrt{5}$

#### Explanation:

$\sqrt{\frac{400}{5}} = \frac{\sqrt{400}}{\sqrt{5}} = \frac{20}{\sqrt{5}}$

We want to rationalize the denominator. Here we are just getting rid of the square root, shown in blue.

$\frac{20}{\sqrt{5}} = \frac{20 \textcolor{b l u e}{\sqrt{5}}}{\sqrt{5} \cdot \textcolor{b l u e}{\sqrt{5}}} = \frac{20 \sqrt{5}}{5} = 4 \sqrt{5}$