# How do you simplify sqrt(54p^7)?

Mar 8, 2018

See a solution process below:

#### Explanation:

First, rewrite the term within the radical as:

$\sqrt{9 {p}^{6} \cdot 6 p}$

Now, use this rule for radicals to complete the simplification:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$\sqrt{\textcolor{red}{9 {p}^{6}} \cdot \textcolor{b l u e}{6 p}} \implies$

$\sqrt{\textcolor{red}{9 {p}^{6}}} \cdot \sqrt{\textcolor{b l u e}{6 p}} \implies$

$3 {p}^{3} \sqrt{6 p}$