Simplify square root of 20x^6y^7

$\sqrt{20 x^{6} y^{7}}$

Step 1

Rewrite $20 x^{6} y^{7}$ as ${(2 x^{3} y^{3})}^{2} \cdot (5 y)$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5) x^{6} y^{7}}$

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

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

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

$\sqrt{2^{2} \cdot 5 {(x^{3})}^{2} y^{7}}$

Factor out $y^{6}$ .

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

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

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

Move $5$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 x^{3} y^{3} \sqrt{5 y}$