Simplify ( square root of 16x^3y)/(2x^2y)

$\frac{\sqrt{16 x^{3} y}}{2 x^{2} y}$

Step 1

Simplify the numerator.

Rewrite $16 x^{3} y$ as ${(4 x)}^{2} (x y)$ .

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

$\frac{\sqrt{4^{2} x^{3} y}}{2 x^{2} y}$

Factor out $x^{2}$ .

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

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x \sqrt{x y}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Factor $x$ out of $2 x \sqrt{x y}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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