# What is the sum of the square root of 50 and the square root of 32?

Sep 10, 2015

Assuming only primary (i.e. positive) square roots
$\sqrt{50} + \sqrt{32} = 9 \sqrt{2}$

#### Explanation:

$\sqrt{50} = \sqrt{{5}^{2} \times 2} = \sqrt{{5}^{2}} \times \sqrt{2} = 5 \sqrt{2}$

$\sqrt{32} = \sqrt{{4}^{2} \times 2} = \sqrt{{4}^{2}} \times \sqrt{2} = 4 \sqrt{2}$

$\sqrt{50} + \sqrt{32} = 5 \sqrt{2} + 4 \sqrt{2}$
$\textcolor{w h i t e}{\text{XXXXXXX}} = 9 \sqrt{2}$