Simplify square root of 32x^8

$\sqrt{32 x^{8}}$

Step 1

Rewrite $32 x^{8}$ as ${(4 x^{4})}^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2) x^{8}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 x^{8}}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{4^{2} \cdot 2 {(x^{4})}^{2}}$

Move $2$ .

$\sqrt{4^{2} {(x^{4})}^{2} \cdot 2}$

Rewrite $4^{2} {(x^{4})}^{2}$ as ${(4 x^{4})}^{2}$ .

$\sqrt{{(4 x^{4})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$4 x^{4} \sqrt{2}$