Simplify ( square root of 3)/( square root of xy)

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

Step 1

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

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

Step 2

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 3

Combine using the product rule for radicals.

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