Pre-Algebra Examples

$\sqrt{\frac{1}{99}}$

Step 1

Rewrite $\sqrt{\frac{1}{99}}$ as $\frac{\sqrt{1}}{\sqrt{99}}$ .

$\frac{\sqrt{1}}{\sqrt{99}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{99}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $99$ as $3^{2} \cdot 11$ .

Tap for more steps...

Step 3.1.1

Factor $9$ out of $99$ .

$\frac{1}{\sqrt{9 (11)}}$

Step 3.1.2

Rewrite $9$ as $3^{2}$ .

$\frac{1}{\sqrt{3^{2} \cdot 11}}$

Step 3.2

Pull terms out from under the radical.

$\frac{1}{3 \sqrt{11}}$

Step 4

Multiply $\frac{1}{3 \sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$\frac{1}{3 \sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}}$

Step 5

Combine and simplify the denominator.

Tap for more steps...

Step 5.1

Multiply $\frac{1}{3 \sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$\frac{\sqrt{11}}{3 \sqrt{11} \sqrt{11}}$

Step 5.2

Move $\sqrt{11}$ .

$\frac{\sqrt{11}}{3 (\sqrt{11} \sqrt{11})}$

Step 5.3

Raise $\sqrt{11}$ to the power of $1$ .

$\frac{\sqrt{11}}{3 ({\sqrt{11}}^{1} \sqrt{11})}$

Step 5.4

Raise $\sqrt{11}$ to the power of $1$ .

$\frac{\sqrt{11}}{3 ({\sqrt{11}}^{1} {\sqrt{11}}^{1})}$

Step 5.5

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

$\frac{\sqrt{11}}{3 {\sqrt{11}}^{1 + 1}}$

Step 5.6

Add $1$ and $1$ .

$\frac{\sqrt{11}}{3 {\sqrt{11}}^{2}}$

Step 5.7

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

Tap for more steps...

Step 5.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$\frac{\sqrt{11}}{3 {(11^{\frac{1}{2}})}^{2}}$

Step 5.7.2

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

$\frac{\sqrt{11}}{3 \cdot 11^{\frac{1}{2} \cdot 2}}$

Step 5.7.3

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

$\frac{\sqrt{11}}{3 \cdot 11^{\frac{2}{2}}}$

Step 5.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.7.4.1

Cancel the common factor.

$\frac{\sqrt{11}}{3 \cdot 11^{\frac{2}{2}}}$

Step 5.7.4.2

Rewrite the expression.

$\frac{\sqrt{11}}{3 \cdot 11^{1}}$

Step 5.7.5

Evaluate the exponent.

$\frac{\sqrt{11}}{3 \cdot 11}$

Step 6

Multiply $3$ by $11$ .

$\frac{\sqrt{11}}{33}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{11}}{33}$

Decimal Form:

$0.10050378 \dots$