Simplify square root of (32x^2y)/25

$\sqrt{\frac{32 x^{2} y}{25}}$

Step 1

Rewrite $\frac{32 x^{2} y}{25}$ as ${(\frac{4 x}{5})}^{2} (2 y)$ .

Factor the perfect power ${(4 x)}^{2}$ out of $32 x^{2} y$ .

$\sqrt{\frac{{(4 x)}^{2} \cdot (2 y)}{25}}$

Factor the perfect power $5^{2}$ out of $25$ .

$\sqrt{\frac{{(4 x)}^{2} \cdot (2 y)}{5^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(4 x)}^{2} \cdot (2 y)}{5^{2} \cdot 1}$ .

$\sqrt{{(\frac{4 x}{5})}^{2} (2 y)}$

Step 2

Pull terms out from under the radical.

$\frac{4 x}{5} \sqrt{2 y}$

Step 3

Combine $\frac{4 x}{5}$ and $\sqrt{2 y}$ .

$\frac{4 x \sqrt{2 y}}{5}$