Simplify the Radical Expression (3x)/(4y) square root of x^3y^4

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

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

Factor out $x^{2}$ .

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

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

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

Move $x$ .

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

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

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

Cancel the common factor of $y$ .

Factor $y$ out of $4 y$ .

$\frac{3 x}{y \cdot 4} (y^{2} | x | \sqrt{x})$

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

$\frac{3 x}{y \cdot 4} (y (y | x | \sqrt{x}))$

Cancel the common factor.

$\frac{3 x}{y \cdot 4} (y (y | x | \sqrt{x}))$

Rewrite the expression.

$\frac{3 x}{4} (y | x | \sqrt{x})$

Combine $y$ and $\frac{3 x}{4}$ .

$\frac{y (3 x)}{4} (| x | \sqrt{x})$

Combine $| x |$ and $\frac{y (3 x)}{4}$ .

$\frac{| x | (y (3 x))}{4} \sqrt{x}$

Combine $\frac{| x | (y (3 x))}{4}$ and $\sqrt{x}$ .

$\frac{| x | (y (3 x)) \sqrt{x}}{4}$

Remove unnecessary parentheses.

$\frac{| x | y \cdot 3 x \sqrt{x}}{4}$

Move $3$ to the left of $| x | y$ .

$\frac{3 \cdot (| x | y) x \sqrt{x}}{4}$

Reorder factors in $\frac{3 | x | y x \sqrt{x}}{4}$ .

$\frac{3 y x | x | \sqrt{x}}{4}$