Simplify ( square root of 18x^2y)/( square root of 2y^3)

$\frac{\sqrt{18 x^{2} y}}{\sqrt{2 y^{3}}}$

Step 1

Combine $\sqrt{18 x^{2} y}$ and $\sqrt{2 y^{3}}$ into a single radical.

$\sqrt{\frac{18 x^{2} y}{2 y^{3}}}$

Step 2

Reduce the expression $\frac{18 x^{2} y}{2 y^{3}}$ by cancelling the common factors.

Factor $2$ out of $18 x^{2} y$ .

$\sqrt{\frac{2 (9 x^{2} y)}{2 y^{3}}}$

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

$\sqrt{\frac{2 (9 x^{2} y)}{2 (y^{3})}}$

Cancel the common factor.

$\sqrt{\frac{2 (9 x^{2} y)}{2 y^{3}}}$

Rewrite the expression.

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

Step 3

Cancel the common factor of $y$ and $y^{3}$ .

Factor $y$ out of $9 x^{2} y$ .

$\sqrt{\frac{y (9 x^{2})}{y^{3}}}$

Cancel the common factors.

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

$\sqrt{\frac{y (9 x^{2})}{y \cdot y^{2}}}$

Cancel the common factor.

$\sqrt{\frac{y (9 x^{2})}{y \cdot y^{2}}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{2}}{y^{2}}}$

Step 4

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

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

Step 5

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

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

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3 x}{y}$