# How do you simplify ( 2 square root x) ( 5 square root x^3 )?

Sep 30, 2015

$10 {x}^{2}$

#### Explanation:

$\left(2 \sqrt{x}\right) \left(5 \sqrt{{x}^{3}}\right)$

Since both factors have the same index (2), you can combine them into one radical symbol.

$\left(2 \sqrt{x}\right) \left(5 \sqrt{{x}^{3}}\right)$
$= \left(2 \cdot 5\right) \cdot \sqrt{x \cdot {x}^{3}}$
$= 10 \cdot \sqrt{{x}^{4}}$
$= 10 \sqrt{{x}^{2} \cdot {x}^{2}}$
$= \textcolor{red}{10 {x}^{2}}$