Algebra Examples

\frac{3}{\sqrt{13}}

$\frac{3}{\sqrt{13}}$

Step 1

Multiply

\frac{3}{\sqrt{13}}

$\frac{3}{\sqrt{13}}$ by

\frac{\sqrt{13}}{\sqrt{13}}

$\frac{\sqrt{13}}{\sqrt{13}}$ .

\frac{3}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}

$\frac{3}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply

\frac{3}{\sqrt{13}}

$\frac{3}{\sqrt{13}}$ by

\frac{\sqrt{13}}{\sqrt{13}}

$\frac{\sqrt{13}}{\sqrt{13}}$ .

\frac{3 \sqrt{13}}{\sqrt{13} \sqrt{13}}

$\frac{3 \sqrt{13}}{\sqrt{13} \sqrt{13}}$

Step 2.2

Raise

\sqrt{13}

$\sqrt{13}$ to the power of

1

$1$ .

\frac{3 \sqrt{13}}{{\sqrt{13}}^{1} \sqrt{13}}

$\frac{3 \sqrt{13}}{{\sqrt{13}}^{1} \sqrt{13}}$

Step 2.3

Raise

\sqrt{13}

$\sqrt{13}$ to the power of

1

$1$ .

\frac{3 \sqrt{13}}{{\sqrt{13}}^{1} {\sqrt{13}}^{1}}

$\frac{3 \sqrt{13}}{{\sqrt{13}}^{1} {\sqrt{13}}^{1}}$

Step 2.4

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{3 \sqrt{13}}{{\sqrt{13}}^{1 + 1}}

$\frac{3 \sqrt{13}}{{\sqrt{13}}^{1 + 1}}$

Step 2.5

Add

1

$1$ and

1

$1$ .

\frac{3 \sqrt{13}}{{\sqrt{13}}^{2}}

$\frac{3 \sqrt{13}}{{\sqrt{13}}^{2}}$

Step 2.6

Rewrite

{\sqrt{13}}^{2}

${\sqrt{13}}^{2}$ as

13

$13$ .

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Step 2.6.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{13}

$\sqrt{13}$ as

13^{\frac{1}{2}}

$13^{\frac{1}{2}}$ .

\frac{3 \sqrt{13}}{{(13^{\frac{1}{2}})}^{2}}

$\frac{3 \sqrt{13}}{{(13^{\frac{1}{2}})}^{2}}$

Step 2.6.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{3 \sqrt{13}}{13^{\frac{1}{2} \cdot 2}}

$\frac{3 \sqrt{13}}{13^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

\frac{3 \sqrt{13}}{13^{\frac{2}{2}}}

$\frac{3 \sqrt{13}}{13^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of

2

$2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{3 \sqrt{13}}{13^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{3 \sqrt{13}}{13^{1}}$

$\frac{3 \sqrt{13}}{13^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{3 \sqrt{13}}{13}$

$\frac{3 \sqrt{13}}{13}$

$\frac{3 \sqrt{13}}{13}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{13}}{13}$

Decimal Form:

$0.83205029 \dots$

$\frac{3}{\sqrt[]{13}}$

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