How do you simplify root3(250 x^8 y^4)?

Jun 18, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

$\sqrt[3]{125 {x}^{6} {y}^{3} \cdot 2 {x}^{2} y}$

Now, use this rule of radicals to simplify the expression:

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

$\sqrt[3]{\textcolor{red}{125 {x}^{6} {y}^{3}} \cdot \textcolor{b l u e}{2 {x}^{2} y}} = \sqrt[3]{\textcolor{red}{125 {x}^{6} {y}^{3}}} \cdot \sqrt[3]{\textcolor{b l u e}{2 {x}^{2} y}} = 5 {x}^{2} y \sqrt[3]{2 {x}^{2} y}$