Basic Math Examples

$\frac{1}{240 \sqrt{\frac{1}{320 π}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $\sqrt{\frac{1}{320 π}}$ as $\frac{\sqrt{1}}{\sqrt{320 π}}$ .

$\frac{1}{240 \frac{\sqrt{1}}{\sqrt{320 π}}}$

Step 1.2

Any root of $1$ is $1$ .

$\frac{1}{240 \frac{1}{\sqrt{320 π}}}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $320 π$ as $8^{2} \cdot (5 π)$ .

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Step 1.3.1.1

Factor $64$ out of $320$ .

$\frac{1}{240 \frac{1}{\sqrt{64 (5) π}}}$

Step 1.3.1.2

Rewrite $64$ as $8^{2}$ .

$\frac{1}{240 \frac{1}{\sqrt{8^{2} \cdot 5 π}}}$

Step 1.3.1.3

Add parentheses.

$\frac{1}{240 \frac{1}{\sqrt{8^{2} \cdot (5 π)}}}$

Step 1.3.2

Pull terms out from under the radical.

$\frac{1}{240 \frac{1}{8 \sqrt{5 π}}}$

Step 1.4

Multiply $\frac{1}{8 \sqrt{5 π}}$ by $\frac{\sqrt{5 π}}{\sqrt{5 π}}$ .

$\frac{1}{240 (\frac{1}{8 \sqrt{5 π}} \cdot \frac{\sqrt{5 π}}{\sqrt{5 π}})}$

Step 1.5

Combine and simplify the denominator.

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Step 1.5.1

Multiply $\frac{1}{8 \sqrt{5 π}}$ by $\frac{\sqrt{5 π}}{\sqrt{5 π}}$ .

$\frac{1}{240 \frac{\sqrt{5 π}}{8 \sqrt{5 π} \sqrt{5 π}}}$

Step 1.5.2

Move $\sqrt{5 π}$ .

$\frac{1}{240 \frac{\sqrt{5 π}}{8 (\sqrt{5 π} \sqrt{5 π})}}$

Step 1.5.3

Raise $\sqrt{5 π}$ to the power of $1$ .

$\frac{1}{240 \frac{\sqrt{5 π}}{8 ({\sqrt{5 π}}^{1} \sqrt{5 π})}}$

Step 1.5.4

Raise $\sqrt{5 π}$ to the power of $1$ .

$\frac{1}{240 \frac{\sqrt{5 π}}{8 ({\sqrt{5 π}}^{1} {\sqrt{5 π}}^{1})}}$

Step 1.5.5

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

$\frac{1}{240 \frac{\sqrt{5 π}}{8 {\sqrt{5 π}}^{1 + 1}}}$

Step 1.5.6

Add $1$ and $1$ .

$\frac{1}{240 \frac{\sqrt{5 π}}{8 {\sqrt{5 π}}^{2}}}$

Step 1.5.7

Rewrite ${\sqrt{5 π}}^{2}$ as $5 π$ .

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Step 1.5.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 π}$ as ${(5 π)}^{\frac{1}{2}}$ .

$\frac{1}{240 \frac{\sqrt{5 π}}{8 {({(5 π)}^{\frac{1}{2}})}^{2}}}$

Step 1.5.7.2

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

$\frac{1}{240 \frac{\sqrt{5 π}}{8 {(5 π)}^{\frac{1}{2} \cdot 2}}}$

Step 1.5.7.3

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

$\frac{1}{240 \frac{\sqrt{5 π}}{8 {(5 π)}^{\frac{2}{2}}}}$

Step 1.5.7.4

Cancel the common factor of $2$ .

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Step 1.5.7.4.1

Cancel the common factor.

$\frac{1}{240 \frac{\sqrt{5 π}}{8 {(5 π)}^{\frac{2}{2}}}}$

Step 1.5.7.4.2

Rewrite the expression.

$\frac{1}{240 \frac{\sqrt{5 π}}{8 {(5 π)}^{1}}}$

Step 1.5.7.5

Simplify.

$\frac{1}{240 \frac{\sqrt{5 π}}{8 (5 π)}}$

Step 1.6

Multiply $8$ by $5$ .

$\frac{1}{240 \frac{\sqrt{5 π}}{40 π}}$

Step 2

Simplify terms.

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Step 2.1

Combine $240$ and $\frac{\sqrt{5 π}}{40 π}$ .

$\frac{1}{\frac{240 \sqrt{5 π}}{40 π}}$

Step 2.2

Reduce the expression $\frac{240 \sqrt{5 π}}{40 π}$ by cancelling the common factors.

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Step 2.2.1

Factor $40$ out of $240 \sqrt{5 π}$ .

$\frac{1}{\frac{40 (6 \sqrt{5 π})}{40 π}}$

Step 2.2.2

Factor $40$ out of $40 π$ .

$\frac{1}{\frac{40 (6 \sqrt{5 π})}{40 (π)}}$

Step 2.2.3

Cancel the common factor.

$\frac{1}{\frac{40 (6 \sqrt{5 π})}{40 π}}$

Step 2.2.4

Rewrite the expression.

$\frac{1}{\frac{6 \sqrt{5 π}}{π}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{π}{6 \sqrt{5 π}}$

Step 4

Multiply $\frac{π}{6 \sqrt{5 π}}$ by $1$ .

$\frac{π}{6 \sqrt{5 π}}$

Step 5

Multiply $\frac{π}{6 \sqrt{5 π}}$ by $\frac{\sqrt{5 π}}{\sqrt{5 π}}$ .

$\frac{π}{6 \sqrt{5 π}} \cdot \frac{\sqrt{5 π}}{\sqrt{5 π}}$

Step 6

Simplify terms.

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Step 6.1

Combine and simplify the denominator.

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Step 6.1.1

Multiply $\frac{π}{6 \sqrt{5 π}}$ by $\frac{\sqrt{5 π}}{\sqrt{5 π}}$ .

$\frac{π \sqrt{5 π}}{6 \sqrt{5 π} \sqrt{5 π}}$

Step 6.1.2

Move $\sqrt{5 π}$ .

$\frac{π \sqrt{5 π}}{6 (\sqrt{5 π} \sqrt{5 π})}$

Step 6.1.3

Raise $\sqrt{5 π}$ to the power of $1$ .

$\frac{π \sqrt{5 π}}{6 ({\sqrt{5 π}}^{1} \sqrt{5 π})}$

Step 6.1.4

Raise $\sqrt{5 π}$ to the power of $1$ .

$\frac{π \sqrt{5 π}}{6 ({\sqrt{5 π}}^{1} {\sqrt{5 π}}^{1})}$

Step 6.1.5

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

$\frac{π \sqrt{5 π}}{6 {\sqrt{5 π}}^{1 + 1}}$

Step 6.1.6

Add $1$ and $1$ .

$\frac{π \sqrt{5 π}}{6 {\sqrt{5 π}}^{2}}$

Step 6.1.7

Rewrite ${\sqrt{5 π}}^{2}$ as $5 π$ .

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Step 6.1.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 π}$ as ${(5 π)}^{\frac{1}{2}}$ .

$\frac{π \sqrt{5 π}}{6 {({(5 π)}^{\frac{1}{2}})}^{2}}$

Step 6.1.7.2

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

$\frac{π \sqrt{5 π}}{6 {(5 π)}^{\frac{1}{2} \cdot 2}}$

Step 6.1.7.3

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

$\frac{π \sqrt{5 π}}{6 {(5 π)}^{\frac{2}{2}}}$

Step 6.1.7.4

Cancel the common factor of $2$ .

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Step 6.1.7.4.1

Cancel the common factor.

$\frac{π \sqrt{5 π}}{6 {(5 π)}^{\frac{2}{2}}}$

Step 6.1.7.4.2

Rewrite the expression.

$\frac{π \sqrt{5 π}}{6 {(5 π)}^{1}}$

Step 6.1.7.5

Simplify.

$\frac{π \sqrt{5 π}}{6 (5 π)}$

Step 6.2

Cancel the common factor of $π$ .

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Step 6.2.1

Cancel the common factor.

$\frac{π \sqrt{5 π}}{6 (5 π)}$

Step 6.2.2

Rewrite the expression.

$\frac{\sqrt{5 π}}{6 \cdot (5)}$

Step 7

Multiply $6$ by $5$ .

$\frac{\sqrt{5 π}}{30}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{5 π}}{30}$

Decimal Form:

$0.13211090 \dots$