Simplify square root of 4x^9

$\sqrt{4 x^{9}}$

Step 1

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

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

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

Factor out $x^{8}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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