# What is the square root of 5 times the square root of 10?

Sep 10, 2015

$\sqrt{5} \cdot \sqrt{10} = 5 \sqrt{2}$
(assuming only primary roots; otherwise $- 5 \sqrt{2}$ is a secondary answer)

#### Explanation:

$\sqrt{5} \cdot \textcolor{red}{\sqrt{10}}$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{5} \cdot \textcolor{red}{\sqrt{5} \cdot \sqrt{2}}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{b l u e}{\sqrt{5} \cdot \sqrt{5}} \cdot \sqrt{2}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{b l u e}{5} \sqrt{2}$