# How do you simplify sqrt(50a^8)?

Mar 18, 2018

$5 {a}^{4} \sqrt{2}$

#### Explanation:

We can separate the radical into the following:

$\textcolor{b l u e}{\sqrt{50}} \cdot \sqrt{{a}^{8}}$

We can factor a $\sqrt{25}$ out of $\sqrt{50}$. We get:

$\textcolor{b l u e}{\sqrt{2} \cdot \sqrt{25}} \cdot \sqrt{{a}^{8}}$

Which can be simplified as

$\textcolor{b l u e}{5 \sqrt{2}} \cdot \textcolor{red}{\sqrt{{a}^{8}}}$

Which can be simplified as

$5 \sqrt{2} \cdot \textcolor{red}{{a}^{4}}$

Thus, we have

$5 {a}^{4} \sqrt{2}$