Simplify ( square root of 25x^3y^4)/(2x^4y)

$\frac{\sqrt{25 x^{3} y^{4}}}{2 x^{4} y}$

Simplify the numerator.

Rewrite $25 x^{3} y^{4}$ as ${(5 x y^{2})}^{2} x$ .

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

$\frac{\sqrt{5^{2} x^{3} y^{4}}}{2 x^{4} y}$

Factor out $x^{2}$ .

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

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

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

Move $x$ .

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

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

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

Pull terms out from under the radical.

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ and $x^{4}$ .

Factor $x$ out of $5 x y^{2} \sqrt{x}$ .

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

Cancel the common factors.

Factor $x$ out of $2 x^{4} y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $y$ out of $5 y^{2} \sqrt{x}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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