Simplify square root of x^2y^5

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

Step 1

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

Factor out $y^{4}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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