Simplify square root of x^3y^5

$\sqrt{x^{3} y^{5}}$

Rewrite $x^{3} y^{5}$ as ${(x y^{2})}^{2} (x y)$ .

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Factor out $x^{2}$ .

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

Factor out $y^{4}$ .

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

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

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

Move $x$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Simplify square root of x^3y^5

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