Simplify square root of 8x^3y^2

$\sqrt{8 x^{3} y^{2}}$

Step 1

Rewrite $8 x^{3} y^{2}$ as ${(2 x y)}^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

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

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

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

Factor out $x^{2}$ .

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 x y \sqrt{2 x}$