Simplify 3y^2 square root of 180x^3y^6

$3 y^{2} \sqrt{180 x^{3} y^{6}}$

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

Factor $36$ out of $180$ .

$3 y^{2} \sqrt{36 (5) x^{3} y^{6}}$

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

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

Factor out $x^{2}$ .

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

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

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

Move $x$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $3$ and $2$ .

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

Multiply $6$ by $3$ .

$18 y^{5} x \sqrt{5 x}$