Simplify square root of 200x^2y

$\sqrt{200 x^{2} y}$

Step 1

Rewrite $200 x^{2} y$ as ${(10 x)}^{2} \cdot (2 y)$ .

Factor $100$ out of $200$ .

$\sqrt{100 (2) x^{2} y}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 2 x^{2} y}$

Move $2$ .

$\sqrt{10^{2} x^{2} \cdot 2 y}$

Rewrite $10^{2} x^{2}$ as ${(10 x)}^{2}$ .

$\sqrt{{(10 x)}^{2} \cdot 2 y}$

Add parentheses.

$\sqrt{{(10 x)}^{2} \cdot (2 y)}$

Step 2

Pull terms out from under the radical.

$10 x \sqrt{2 y}$