Simplify square root of 64x^9

$\sqrt{64 x^{9}}$

Step 1

Rewrite $64 x^{9}$ as ${(8 x^{4})}^{2} x$ .

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} x^{9}}$

Factor out $x^{8}$ .

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

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

$\sqrt{8^{2} ({(x^{4})}^{2} x)}$

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

$\sqrt{{(8 x^{4})}^{2} x}$

Step 2

Pull terms out from under the radical.

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