Simplify square root of (64x^3y)/(2x^2)

$\sqrt{\frac{64 x^{3} y}{2 x^{2}}}$

Step 1

Reduce the expression $\frac{64 x^{3} y}{2 x^{2}}$ by cancelling the common factors.

Factor $2$ out of $64 x^{3} y$ .

$\sqrt{\frac{2 (32 x^{3} y)}{2 x^{2}}}$

Factor $2$ out of $2 x^{2}$ .

$\sqrt{\frac{2 (32 x^{3} y)}{2 (x^{2})}}$

Cancel the common factor.

$\sqrt{\frac{2 (32 x^{3} y)}{2 x^{2}}}$

Rewrite the expression.

$\sqrt{\frac{32 x^{3} y}{x^{2}}}$

Step 2

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $32 x^{3} y$ .

$\sqrt{\frac{x^{2} (32 x y)}{x^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{2} (32 x y)}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (32 x y)}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{32 x y}{1}}$

Divide $32 x y$ by $1$ .

$\sqrt{32 x y}$

Step 3

Rewrite $32 x y$ as ${(2^{2})}^{2} \cdot (2 x y)$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2) x y}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 x y}$

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

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

Add parentheses.

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Raise $2$ to the power of $2$ .

$4 \sqrt{2 x y}$