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

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

Step 1

Combine $\sqrt{25 x^{2} y^{2}}$ and $\sqrt{x y}$ into a single radical.

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

Step 2

Reduce the expression $\frac{25 x^{2} y^{2}}{x y}$ by cancelling the common factors.

Factor $x$ out of $25 x^{2} y^{2}$ .

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

Factor $x$ out of $x y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

Factor $y$ out of $25 x y^{2}$ .

$\sqrt{\frac{y (25 x y)}{y}}$

Cancel the common factors.

Raise $y$ to the power of $1$ .

$\sqrt{\frac{y (25 x y)}{y^{1}}}$

Factor $y$ out of $y^{1}$ .

$\sqrt{\frac{y (25 x y)}{y \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y (25 x y)}{y \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{25 x y}{1}}$

Divide $25 x y$ by $1$ .

$\sqrt{25 x y}$

Step 4

Rewrite $25 x y$ as $5^{2} (x y)$ .

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

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

Add parentheses.

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

Step 5

Pull terms out from under the radical.

$5 \sqrt{x y}$