Simplify square root of 180x^6y^15

$\sqrt{180 x^{6} y^{15}}$

Step 1

Rewrite $180 x^{6} y^{15}$ as ${(6 x^{3} y^{7})}^{2} \cdot (5 y)$ .

Factor $36$ out of $180$ .

$\sqrt{36 (5) x^{6} y^{15}}$

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

$\sqrt{6^{2} \cdot 5 x^{6} y^{15}}$

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

$\sqrt{6^{2} \cdot 5 {(x^{3})}^{2} y^{15}}$

Factor out $y^{14}$ .

$\sqrt{6^{2} \cdot 5 {(x^{3})}^{2} (y^{14} y)}$

Rewrite $y^{14}$ as ${(y^{7})}^{2}$ .

$\sqrt{6^{2} \cdot 5 {(x^{3})}^{2} ({(y^{7})}^{2} y)}$

Move $5$ .

$\sqrt{6^{2} {(x^{3})}^{2} {(y^{7})}^{2} \cdot 5 y}$

Rewrite $6^{2} {(x^{3})}^{2} {(y^{7})}^{2}$ as ${(6 x^{3} y^{7})}^{2}$ .

$\sqrt{{(6 x^{3} y^{7})}^{2} \cdot 5 y}$

Add parentheses.

$\sqrt{{(6 x^{3} y^{7})}^{2} \cdot (5 y)}$

Step 2

Pull terms out from under the radical.

$6 x^{3} y^{7} \sqrt{5 y}$