Basic Math Examples

\frac{24}{\sqrt{30}}

$\frac{24}{\sqrt{30}}$

Step 1

Multiply

\frac{24}{\sqrt{30}}

$\frac{24}{\sqrt{30}}$ by

\frac{\sqrt{30}}{\sqrt{30}}

$\frac{\sqrt{30}}{\sqrt{30}}$ .

\frac{24}{\sqrt{30}} \cdot \frac{\sqrt{30}}{\sqrt{30}}

$\frac{24}{\sqrt{30}} \cdot \frac{\sqrt{30}}{\sqrt{30}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply

\frac{24}{\sqrt{30}}

$\frac{24}{\sqrt{30}}$ by

\frac{\sqrt{30}}{\sqrt{30}}

$\frac{\sqrt{30}}{\sqrt{30}}$ .

\frac{24 \sqrt{30}}{\sqrt{30} \sqrt{30}}

$\frac{24 \sqrt{30}}{\sqrt{30} \sqrt{30}}$

Step 2.2

Raise

\sqrt{30}

$\sqrt{30}$ to the power of

1

$1$ .

\frac{24 \sqrt{30}}{{\sqrt{30}}^{1} \sqrt{30}}

$\frac{24 \sqrt{30}}{{\sqrt{30}}^{1} \sqrt{30}}$

Step 2.3

Raise

\sqrt{30}

$\sqrt{30}$ to the power of

1

$1$ .

\frac{24 \sqrt{30}}{{\sqrt{30}}^{1} {\sqrt{30}}^{1}}

$\frac{24 \sqrt{30}}{{\sqrt{30}}^{1} {\sqrt{30}}^{1}}$

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{24 \sqrt{30}}{{\sqrt{30}}^{1 + 1}}

$\frac{24 \sqrt{30}}{{\sqrt{30}}^{1 + 1}}$

Step 2.5

Add

1

$1$ and

1

$1$ .

\frac{24 \sqrt{30}}{{\sqrt{30}}^{2}}

$\frac{24 \sqrt{30}}{{\sqrt{30}}^{2}}$

Step 2.6

Rewrite

{\sqrt{30}}^{2}

${\sqrt{30}}^{2}$ as

30

$30$ .

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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{30}

$\sqrt{30}$ as

30^{\frac{1}{2}}

$30^{\frac{1}{2}}$ .

\frac{24 \sqrt{30}}{{(30^{\frac{1}{2}})}^{2}}

$\frac{24 \sqrt{30}}{{(30^{\frac{1}{2}})}^{2}}$

Step 2.6.2

Apply the power rule and multiply exponents,

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

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

\frac{24 \sqrt{30}}{30^{\frac{1}{2} \cdot 2}}

$\frac{24 \sqrt{30}}{30^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

\frac{24 \sqrt{30}}{30^{\frac{2}{2}}}

$\frac{24 \sqrt{30}}{30^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of

2

$2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{24 \sqrt{30}}{30^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{24 \sqrt{30}}{30^{1}}$

$\frac{24 \sqrt{30}}{30^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{24 \sqrt{30}}{30}$

$\frac{24 \sqrt{30}}{30}$

$\frac{24 \sqrt{30}}{30}$

Step 3

Cancel the common factor of

$24$ and

$30$ .

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Step 3.1

Factor

$6$ out of

$24 \sqrt{30}$ .

$\frac{6 (4 \sqrt{30})}{30}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

$6$ out of

$30$ .

$\frac{6 (4 \sqrt{30})}{6 (5)}$

Step 3.2.2

Cancel the common factor.

$\frac{6 (4 \sqrt{30})}{6 \cdot 5}$

Step 3.2.3

Rewrite the expression.

$\frac{4 \sqrt{30}}{5}$

$\frac{4 \sqrt{30}}{5}$

$\frac{4 \sqrt{30}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{30}}{5}$

Decimal Form:

$4.38178046 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$