# What is -4 square root of 90 + 2 square root of 160?

Sep 16, 2015

$- 4 \sqrt{10}$

#### Explanation:

$\sqrt{90}$
$\textcolor{w h i t e}{\text{XX}} = \sqrt{{3}^{2} \times 10} = 3 \sqrt{10}$

$\sqrt{160}$
$\textcolor{w h i t e}{\text{XX}} = \sqrt{{4}^{2} \times 10} = 4 \sqrt{10}$

Therefore
$\textcolor{red}{- 4 \sqrt{90}} + \textcolor{b l u e}{2 \sqrt{160}}$

$\textcolor{w h i t e}{\text{XX}} = \textcolor{red}{\left(- 4\right) \left(3 \sqrt{10}\right)} + \textcolor{b l u e}{\left(2\right) \left(4 \sqrt{10}\right)}$

$\textcolor{w h i t e}{\text{XX}} = \textcolor{red}{- 12 \sqrt{10}} + \textcolor{b l u e}{8 \sqrt{10}}$

$\textcolor{w h i t e}{\text{XX}} = - 4 \sqrt{10}$