# How do you find the square root of 405?

Sep 16, 2015

$\sqrt{405} = 9 \sqrt{5}$

#### Explanation:

Taking the prime factors of $405$:

$= 3 \times 135$
$= \textcolor{red}{3 \times 3} \times 45$
$= \textcolor{red}{3 \times 3} \times 3 \times 15$
$= \textcolor{red}{3 \times 3} \times \textcolor{b l u e}{3 \times 3} \times 5$
$= \textcolor{red}{{3}^{2}} \times \textcolor{b l u e}{{3}^{2}} \times \textcolor{g r e e n}{5}$

$\sqrt{405}$

=sqrt(color(red)(3^2)*color(blue)(3^2)*color(green)(5)
$= \sqrt{\textcolor{red}{{3}^{2}}} \cdot \sqrt{\textcolor{b l u e}{{3}^{2}}} \cdot \sqrt{\textcolor{g r e e n}{5}}$
$= \textcolor{red}{3} \cdot \textcolor{b l u e}{3} \cdot \sqrt{\textcolor{g r e e n}{5}}$
$= 9 \sqrt{5}$