Simplify square root of 80x^7y^6

$\sqrt{80 x^{7} y^{6}}$

Step 1

Rewrite $80 x^{7} y^{6}$ as ${(4 x^{3} y^{3})}^{2} \cdot (5 x)$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) x^{7} y^{6}}$

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

$\sqrt{4^{2} \cdot 5 x^{7} y^{6}}$

Factor out $x^{6}$ .

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

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{4^{2} \cdot 5 ({(x^{3})}^{2} x) y^{6}}$

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$\sqrt{4^{2} \cdot 5 ({(x^{3})}^{2} x) {(y^{3})}^{2}}$

Move $x$ .

$\sqrt{4^{2} \cdot 5 ({(x^{3})}^{2}) {(y^{3})}^{2} x}$

Move $5$ .

$\sqrt{4^{2} ({(x^{3})}^{2}) {(y^{3})}^{2} \cdot 5 x}$

Rewrite $(4^{2} ({(x^{3})}^{2})) {(y^{3})}^{2}$ as ${(4 x^{3} y^{3})}^{2}$ .

$\sqrt{{(4 x^{3} y^{3})}^{2} \cdot 5 x}$

Add parentheses.

$\sqrt{{(4 x^{3} y^{3})}^{2} \cdot (5 x)}$

Step 2

Pull terms out from under the radical.

$4 x^{3} y^{3} \sqrt{5 x}$