Simplify square root of 32x^9y^5

$\sqrt{32 x^{9} y^{5}}$

Step 1

Rewrite $32 x^{9} y^{5}$ as ${(4 x^{4} y^{2})}^{2} \cdot (2 x y)$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2) x^{9} y^{5}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 x^{9} y^{5}}$

Factor out $x^{8}$ .

$\sqrt{4^{2} \cdot 2 (x^{8} x) y^{5}}$

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

$\sqrt{4^{2} \cdot 2 ({(x^{4})}^{2} x) y^{5}}$

Factor out $y^{4}$ .

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

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

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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