Simplify square root of 162x^3y^2

$\sqrt{162 x^{3} y^{2}}$

Step 1

Rewrite $162 x^{3} y^{2}$ as ${(9 x y)}^{2} \cdot (2 x)$ .

Factor $81$ out of $162$ .

$\sqrt{81 (2) x^{3} y^{2}}$

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} \cdot 2 x^{3} y^{2}}$

Factor out $x^{2}$ .

$\sqrt{9^{2} \cdot 2 (x^{2} x) y^{2}}$

Move $x$ .

$\sqrt{9^{2} \cdot 2 x^{2} y^{2} x}$

Move $2$ .

$\sqrt{9^{2} x^{2} y^{2} \cdot 2 x}$

Rewrite $(9^{2} (x^{2})) y^{2}$ as ${(9 x y)}^{2}$ .

$\sqrt{{(9 x y)}^{2} \cdot 2 x}$

Add parentheses.

$\sqrt{{(9 x y)}^{2} \cdot (2 x)}$

Step 2

Pull terms out from under the radical.

$9 x y \sqrt{2 x}$