Pre-Algebra Examples

$\sqrt{\frac{1}{29}}$

Step 1

Rewrite $\sqrt{\frac{1}{29}}$ as $\frac{\sqrt{1}}{\sqrt{29}}$ .

$\frac{\sqrt{1}}{\sqrt{29}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{29}}$

Step 3

Multiply $\frac{1}{\sqrt{29}}$ by $\frac{\sqrt{29}}{\sqrt{29}}$ .

$\frac{1}{\sqrt{29}} \cdot \frac{\sqrt{29}}{\sqrt{29}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{1}{\sqrt{29}}$ by $\frac{\sqrt{29}}{\sqrt{29}}$ .

$\frac{\sqrt{29}}{\sqrt{29} \sqrt{29}}$

Step 4.2

Raise $\sqrt{29}$ to the power of $1$ .

$\frac{\sqrt{29}}{{\sqrt{29}}^{1} \sqrt{29}}$

Step 4.3

Raise $\sqrt{29}$ to the power of $1$ .

$\frac{\sqrt{29}}{{\sqrt{29}}^{1} {\sqrt{29}}^{1}}$

Step 4.4

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

$\frac{\sqrt{29}}{{\sqrt{29}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{\sqrt{29}}{{\sqrt{29}}^{2}}$

Step 4.6

Rewrite ${\sqrt{29}}^{2}$ as $29$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{29}$ as $29^{\frac{1}{2}}$ .

$\frac{\sqrt{29}}{{(29^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$\frac{\sqrt{29}}{29^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$\frac{\sqrt{29}}{29^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{\sqrt{29}}{29^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{\sqrt{29}}{29^{1}}$

Step 4.6.5

Evaluate the exponent.

$\frac{\sqrt{29}}{29}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{29}}{29}$

Decimal Form:

$0.18569533 \dots$