Simplify square root of 80x^13y^9

$\sqrt{80 x^{13} y^{9}}$

Step 1

Rewrite $80 x^{13} y^{9}$ as ${(4 x^{6} y^{4})}^{2} \cdot (5 x y)$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) x^{13} y^{9}}$

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

$\sqrt{4^{2} \cdot 5 x^{13} y^{9}}$

Factor out $x^{12}$ .

$\sqrt{4^{2} \cdot 5 (x^{12} x) y^{9}}$

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

$\sqrt{4^{2} \cdot 5 ({(x^{6})}^{2} x) y^{9}}$

Factor out $y^{8}$ .

$\sqrt{4^{2} \cdot 5 ({(x^{6})}^{2} x) (y^{8} y)}$

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

$\sqrt{4^{2} \cdot 5 ({(x^{6})}^{2} x) ({(y^{4})}^{2} y)}$

Move $x$ .

$\sqrt{4^{2} \cdot 5 ({(x^{6})}^{2}) {(y^{4})}^{2} x y}$

Move $5$ .

$\sqrt{4^{2} ({(x^{6})}^{2}) {(y^{4})}^{2} \cdot 5 x y}$

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

$\sqrt{{(4 x^{6} y^{4})}^{2} \cdot 5 x y}$

Add parentheses.

$\sqrt{{(4 x^{6} y^{4})}^{2} \cdot 5 (x y)}$

Add parentheses.

$\sqrt{{(4 x^{6} y^{4})}^{2} \cdot (5 x y)}$

Step 2

Pull terms out from under the radical.

$4 x^{6} y^{4} \sqrt{5 x y}$