Simplify square root of 8x^2y

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

Step 1

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

Factor $4$ out of $8$ .

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

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 x \sqrt{2 y}$