# How do you simplify sqrt(48x^11z^10)?

Oct 23, 2015

$4 {x}^{5} {z}^{5} \sqrt{3 x}$

#### Explanation:

First, factor out all the terms to find any perfect squares.

$\left[1\right] \textcolor{w h i t e}{X X} \sqrt{48 {x}^{11} {z}^{10}}$

$\left[2\right] \textcolor{w h i t e}{X X} = \sqrt{\left(16\right) \left(3\right) \left({x}^{10}\right) \left(x\right) \left({z}^{10}\right)}$

$\left[3\right] \textcolor{w h i t e}{X X} = \sqrt{\left({4}^{2}\right) \left(3\right) {\left({x}^{5}\right)}^{2} \left(x\right) {\left({z}^{5}\right)}^{2}}$

Take all the perfect squares out of the radical symbol.

$\left[4\right] \textcolor{w h i t e}{X X} = \left(4\right) \left({x}^{5}\right) \left({z}^{5}\right) \sqrt{\left(3\right) \left(x\right)}$

[5]color(white)(XX)=color(blue)(4x^5z^5sqrt(3x)