Simplify square root of x^4y^11

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

Step 1

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

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

$\sqrt{{(x^{2})}^{2} y^{11}}$

Factor out $y^{10}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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