# What is the square root of 10 times the square root of 40?

May 9, 2018

#### Explanation:

One of the properties of square roots is

$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$

as long as $a$ and $b$ are non-negative real numbers.

So:

$\sqrt{10} \times \sqrt{40} = \sqrt{10 \times 40}$
$\textcolor{w h i t e}{\sqrt{10} \times \sqrt{40}} = \sqrt{400}$
$\textcolor{w h i t e}{\sqrt{10} \times \sqrt{40}} = 20$

since ${20}^{2} = 400$.