# How do you simplify 4sqrt(32x^8 y^3 z^10)?

Apr 13, 2018

$16 \sqrt{2} {x}^{4} {y}^{1.5} {z}^{5}$

#### Explanation:

Rewrite $32$ as ${2}^{5}$ and $4$ as ${2}^{2}$ to more easily group numbers together.

${2}^{2} \sqrt{{2}^{5} {x}^{8} {y}^{3} {z}^{10}}$

The square root will halve all of the powers of the factors inside the radical.

${2}^{2} \times {2}^{2.5} {x}^{4} {y}^{1.5} {z}^{5}$

${2}^{4.5} {x}^{4} {y}^{1.5} {z}^{5}$

$16 \sqrt{2} {x}^{4} {y}^{1.5} {z}^{5}$