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

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

Step 1

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

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

Step 2

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

Factor $2$ out of $18 y^{3}$ .

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

Factor $2$ out of $2 y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

Factor $y$ out of $9 y^{3}$ .

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

Cancel the common factors.

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

$\sqrt{\frac{y (9 y^{2})}{y^{1}}}$

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

$\sqrt{\frac{y (9 y^{2})}{y \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y (9 y^{2})}{y \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{9 y^{2}}{1}}$

Divide $9 y^{2}$ by $1$ .

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

Step 4

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

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

Step 5

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

$3 y$