Simplify square root of 81/x

$\sqrt{\frac{81}{x}}$

Step 1

Rewrite $\sqrt{\frac{81}{x}}$ as $\frac{\sqrt{81}}{\sqrt{x}}$ .

$\frac{\sqrt{81}}{\sqrt{x}}$

Step 2

Simplify the numerator.

Rewrite $81$ as $9^{2}$ .

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

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

$\frac{9}{\sqrt{x}}$

Step 3

Multiply $\frac{9}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{9}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Step 4

Combine and simplify the denominator.

Multiply $\frac{9}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{9 \sqrt{x}}{\sqrt{x} \sqrt{x}}$

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

$\frac{9 \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}}$

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

$\frac{9 \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}}$

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

$\frac{9 \sqrt{x}}{{\sqrt{x}}^{1 + 1}}$

Add $1$ and $1$ .

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

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

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

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

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

$\frac{9 \sqrt{x}}{x^{\frac{1}{2} \cdot 2}}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{9 \sqrt{x}}{x^{1}}$

Simplify.

$\frac{9 \sqrt{x}}{x}$