Simplify square root of 36x^9y^25

$\sqrt{36 x^{9} y^{25}}$

Step 1

Rewrite $36 x^{9} y^{25}$ as ${(6 x^{4} y^{12})}^{2} (x y)$ .

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} x^{9} y^{25}}$

Factor out $x^{8}$ .

$\sqrt{6^{2} (x^{8} x) y^{25}}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{6^{2} ({(x^{4})}^{2} x) y^{25}}$

Factor out $y^{24}$ .

$\sqrt{6^{2} ({(x^{4})}^{2} x) (y^{24} y)}$

Rewrite $y^{24}$ as ${(y^{12})}^{2}$ .

$\sqrt{6^{2} ({(x^{4})}^{2} x) ({(y^{12})}^{2} y)}$

Move $x$ .

$\sqrt{6^{2} ({(x^{4})}^{2}) {(y^{12})}^{2} x y}$

Rewrite $6^{2} ({(x^{4})}^{2}) {(y^{12})}^{2}$ as ${(6 x^{4} y^{12})}^{2}$ .

$\sqrt{{(6 x^{4} y^{12})}^{2} x y}$

Add parentheses.

$\sqrt{{(6 x^{4} y^{12})}^{2} (x y)}$

Step 2

Pull terms out from under the radical.

$6 x^{4} y^{12} \sqrt{x y}$