Simplify ( square root of 9x^5y^3)/(5x^4y^2)

$\frac{\sqrt{9 x^{5} y^{3}}}{5 x^{4} y^{2}}$

Simplify the numerator.

Rewrite $9 x^{5} y^{3}$ as ${(3 x^{2} y)}^{2} (x y)$ .

Rewrite $9$ as $3^{2}$ .

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

Factor out $x^{4}$ .

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

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

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

Factor out $y^{2}$ .

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

Move $x$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{2}$ and $x^{4}$ .

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

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

Cancel the common factors.

Factor $x^{2}$ out of $5 x^{4} y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $y$ out of $3 y \sqrt{x y}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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