Simplify square root of 4x^11

$\sqrt{4 x^{11}}$

Step 1

Rewrite $4 x^{11}$ as ${(2 x^{5})}^{2} x$ .

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

$\sqrt{2^{2} x^{11}}$

Factor out $x^{10}$ .

$\sqrt{2^{2} (x^{10} x)}$

Rewrite $x^{10}$ as ${(x^{5})}^{2}$ .

$\sqrt{2^{2} ({(x^{5})}^{2} x)}$

Rewrite $2^{2} {(x^{5})}^{2}$ as ${(2 x^{5})}^{2}$ .

$\sqrt{{(2 x^{5})}^{2} x}$

Step 2

Pull terms out from under the radical.

$2 x^{5} \sqrt{x}$