Simplify square root of (xy)/(2ab)

$\sqrt{\frac{x y}{2 a b}}$

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

$\frac{\sqrt{x y}}{\sqrt{2 a b}}$

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

$\frac{\sqrt{x y}}{\sqrt{2 a b}} \cdot \frac{\sqrt{2 a b}}{\sqrt{2 a b}}$

Combine and simplify the denominator.

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

$\frac{\sqrt{x y} \sqrt{2 a b}}{\sqrt{2 a b} \sqrt{2 a b}}$

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

$\frac{\sqrt{x y} \sqrt{2 a b}}{{\sqrt{2 a b}}^{1} \sqrt{2 a b}}$

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

$\frac{\sqrt{x y} \sqrt{2 a b}}{{\sqrt{2 a b}}^{1} {\sqrt{2 a b}}^{1}}$

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

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

Add $1$ and $1$ .

$\frac{\sqrt{x y} \sqrt{2 a b}}{{\sqrt{2 a b}}^{2}}$

Rewrite ${\sqrt{2 a b}}^{2}$ as $2 a b$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{\sqrt{x y} \sqrt{2 a b}}{2 a b}$

Combine using the product rule for radicals.

$\frac{\sqrt{x y \cdot 2 a b}}{2 a b}$

Reorder factors in $\frac{\sqrt{x y \cdot 2 a b}}{2 a b}$ .

$\frac{\sqrt{2 x y a b}}{2 a b}$