# How do you simplify sqrt(324)?

Jan 23, 2016

First you factorize the number and then see if you can take any squares out.

#### Explanation:

$324 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3$ (prime factors)
$324 = {2}^{2} \cdot {3}^{4} \mathmr{and} {2}^{2} \cdot {9}^{2}$

$\sqrt{324} = \sqrt{{2}^{2} \cdot {9}^{2}} = \sqrt{{2}^{2}} \cdot \sqrt{{9}^{2}} = 2 \cdot 9 = 18$

${18}^{2} = 364$ check!