# How do you simplify root3(16y^5)?

Jun 17, 2017

See a solution process below:

#### Explanation:

First, we can rewrite the radical as:

$\sqrt[3]{16 {y}^{5}} \implies \sqrt[3]{8 {y}^{3} \cdot 2 {y}^{2}}$

We can now use this rule for radicals to simplify this expression:

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

$\sqrt[3]{\textcolor{red}{8 {y}^{3}} \cdot \textcolor{b l u e}{2 {y}^{2}}} = \sqrt[3]{\textcolor{red}{8 {y}^{3}}} \cdot \sqrt[3]{\textcolor{b l u e}{2 {y}^{2}}} \implies 2 y \sqrt[3]{2 {y}^{2}}$