Simplify square root of 75x^2y

$\sqrt{75 x^{2} y}$

Step 1

Rewrite $75 x^{2} y$ as ${(5 x)}^{2} \cdot (3 y)$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) x^{2} y}$

Rewrite $25$ as $5^{2}$ .

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

Move $3$ .

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

Rewrite $5^{2} x^{2}$ as ${(5 x)}^{2}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$5 x \sqrt{3 y}$