Simplify square root of 4x^13

$\sqrt{4 x^{13}}$

Step 1

Rewrite $4 x^{13}$ as ${(2 x^{6})}^{2} x$ .

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

$\sqrt{2^{2} x^{13}}$

Factor out $x^{12}$ .

$\sqrt{2^{2} (x^{12} x)}$

Rewrite $x^{12}$ as ${(x^{6})}^{2}$ .

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

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

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

Step 2

Pull terms out from under the radical.

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