# How do you simplify sqrt(8x^5) * sqrt(3x)?

Apr 7, 2015

First you try to get the squares out of the root.

I'll do it step by step:

$\sqrt{8 {x}^{5}} \cdot \sqrt{3 x} = \sqrt{{2}^{2} \cdot 2 \cdot {\left({x}^{2}\right)}^{2} \cdot x} \cdot \sqrt{3 x} =$

$2 {x}^{2} \sqrt{2 x} \cdot \sqrt{3 x} = 2 {x}^{2} \sqrt{2 x \cdot 3 x} = 2 {x}^{2} \sqrt{6 \cdot {x}^{2}} =$

$2 {x}^{2} \cdot x \cdot \sqrt{6} = 2 {x}^{3} \sqrt{6}$

OR :

$\sqrt{8 {x}^{5}} \cdot \sqrt{3 x} = \sqrt{8 {x}^{5} \cdot 3 x} =$

$\sqrt{24 {x}^{6}} = \sqrt{{2}^{2} \cdot 6 \cdot {\left({x}^{3}\right)}^{2}} = 2 {x}^{3} \sqrt{6}$