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

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

Step 1

Rewrite $\sqrt{\frac{3 x}{2 y}}$ as $\frac{\sqrt{3 x}}{\sqrt{2 y}}$ .

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

Step 2

Multiply $\frac{\sqrt{3 x}}{\sqrt{2 y}}$ by $\frac{\sqrt{2 y}}{\sqrt{2 y}}$ .

$\frac{\sqrt{3 x}}{\sqrt{2 y}} \cdot \frac{\sqrt{2 y}}{\sqrt{2 y}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3 x}}{\sqrt{2 y}}$ by $\frac{\sqrt{2 y}}{\sqrt{2 y}}$ .

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

Raise $\sqrt{2 y}$ to the power of $1$ .

$\frac{\sqrt{3 x} \sqrt{2 y}}{{\sqrt{2 y}}^{1} \sqrt{2 y}}$

Raise $\sqrt{2 y}$ to the power of $1$ .

$\frac{\sqrt{3 x} \sqrt{2 y}}{{\sqrt{2 y}}^{1} {\sqrt{2 y}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{3 x} \sqrt{2 y}}{{\sqrt{2 y}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{2 y}}^{2}$ as $2 y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 y}$ as ${(2 y)}^{\frac{1}{2}}$ .

$\frac{\sqrt{3 x} \sqrt{2 y}}{{({(2 y)}^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{3 x} \sqrt{2 y}}{{(2 y)}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{\sqrt{3 x} \sqrt{2 y}}{{(2 y)}^{1}}$

Simplify.

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

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

$\frac{\sqrt{6 x y}}{2 y}$