Simplify 3x^2y square root of 180x^4y^3

$3 x^{2} y \sqrt{180 x^{4} y^{3}}$

Rewrite $180 x^{4} y^{3}$ as ${(6 x^{2} y)}^{2} \cdot (5 y)$ .

Factor $36$ out of $180$ .

$3 x^{2} y \sqrt{36 (5) x^{4} y^{3}}$

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

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

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

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

Factor out $y^{2}$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $6$ by $3$ .

$18 x^{4} y^{2} \sqrt{5 y}$