Simplify square root of 4x^7

$\sqrt{4 x^{7}}$

Step 1

Rewrite $4 x^{7}$ as ${(2 x^{3})}^{2} x$ .

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

$\sqrt{2^{2} x^{7}}$

Factor out $x^{6}$ .

$\sqrt{2^{2} (x^{6} x)}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{2^{2} ({(x^{3})}^{2} x)}$

Rewrite $2^{2} {(x^{3})}^{2}$ as ${(2 x^{3})}^{2}$ .

$\sqrt{{(2 x^{3})}^{2} x}$

Step 2

Pull terms out from under the radical.

$2 x^{3} \sqrt{x}$