Basic Math Examples

$\sqrt{\frac{25}{π}}$

Step 1

Rewrite

$\sqrt{\frac{25}{π}}$ as

$\frac{\sqrt{25}}{\sqrt{π}}$ .

$\frac{\sqrt{25}}{\sqrt{π}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite

$25$ as

$5^{2}$ .

$\frac{\sqrt{5^{2}}}{\sqrt{π}}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{5}{\sqrt{π}}$

Step 3

Multiply

$\frac{5}{\sqrt{π}}$ by

$\frac{\sqrt{π}}{\sqrt{π}}$ .

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

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply

$\frac{5}{\sqrt{π}}$ by

$\frac{\sqrt{π}}{\sqrt{π}}$ .

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

Step 4.2

Raise

$\sqrt{π}$ to the power of

$1$ .

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

Step 4.3

Raise

$\sqrt{π}$ to the power of

$1$ .

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

Step 4.4

Use the power rule

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

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

Step 4.5

Add

$1$ and

$1$ .

$\frac{5 \sqrt{π}}{{\sqrt{π}}^{2}}$

Step 4.6

Rewrite

${\sqrt{π}}^{2}$ as

$π$ .

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Step 4.6.1

Use

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

$\sqrt{π}$ as

$π^{\frac{1}{2}}$ .

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

Step 4.6.2

Apply the power rule and multiply exponents,

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

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

Step 4.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{5 \sqrt{π}}{π^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of

$2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{5 \sqrt{π}}{π^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{5 \sqrt{π}}{π^{1}}$

Step 4.6.5

Simplify.

$\frac{5 \sqrt{π}}{π}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{π}}{π}$

Decimal Form:

$2.82094791 \dots$