Basic Math Examples

$25 \div \sqrt{20}$

Step 1

Rewrite the division as a fraction.

$\frac{25}{\sqrt{20}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

$20$ as

$2^{2} \cdot 5$ .

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Step 2.1.1

Factor

$4$ out of

$20$ .

$\frac{25}{\sqrt{4 (5)}}$

Step 2.1.2

Rewrite

$4$ as

$2^{2}$ .

$\frac{25}{\sqrt{2^{2} \cdot 5}}$

$\frac{25}{\sqrt{2^{2} \cdot 5}}$

Step 2.2

Pull terms out from under the radical.

$\frac{25}{2 \sqrt{5}}$

$\frac{25}{2 \sqrt{5}}$

Step 3

Multiply

$\frac{25}{2 \sqrt{5}}$ by

$\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{25}{2 \sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply

$\frac{25}{2 \sqrt{5}}$ by

$\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{25 \sqrt{5}}{2 \sqrt{5} \sqrt{5}}$

Step 4.2

Move

$\sqrt{5}$ .

$\frac{25 \sqrt{5}}{2 (\sqrt{5} \sqrt{5})}$

Step 4.3

Raise

$\sqrt{5}$ to the power of

$1$ .

$\frac{25 \sqrt{5}}{2 ({\sqrt{5}}^{1} \sqrt{5})}$

Step 4.4

Raise

$\sqrt{5}$ to the power of

$1$ .

$\frac{25 \sqrt{5}}{2 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})}$

Step 4.5

Use the power rule

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

$\frac{25 \sqrt{5}}{2 {\sqrt{5}}^{1 + 1}}$

Step 4.6

Add

$1$ and

$1$ .

$\frac{25 \sqrt{5}}{2 {\sqrt{5}}^{2}}$

Step 4.7

Rewrite

${\sqrt{5}}^{2}$ as

$5$ .

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Step 4.7.1

Use

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

$\sqrt{5}$ as

$5^{\frac{1}{2}}$ .

$\frac{25 \sqrt{5}}{2 {(5^{\frac{1}{2}})}^{2}}$

Step 4.7.2

Apply the power rule and multiply exponents,

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

$\frac{25 \sqrt{5}}{2 \cdot 5^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{25 \sqrt{5}}{2 \cdot 5^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of

$2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{25 \sqrt{5}}{2 \cdot 5^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{25 \sqrt{5}}{2 \cdot 5^{1}}$

$\frac{25 \sqrt{5}}{2 \cdot 5^{1}}$

Step 4.7.5

Evaluate the exponent.

$\frac{25 \sqrt{5}}{2 \cdot 5}$

$\frac{25 \sqrt{5}}{2 \cdot 5}$

$\frac{25 \sqrt{5}}{2 \cdot 5}$

Step 5

Cancel the common factor of

$25$ and

$5$ .

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Step 5.1

Factor

$5$ out of

$25 \sqrt{5}$ .

$\frac{5 (5 \sqrt{5})}{2 \cdot 5}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

$5$ out of

$2 \cdot 5$ .

$\frac{5 (5 \sqrt{5})}{5 \cdot 2}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (5 \sqrt{5})}{5 \cdot 2}$

Step 5.2.3

Rewrite the expression.

$\frac{5 \sqrt{5}}{2}$

$\frac{5 \sqrt{5}}{2}$

$\frac{5 \sqrt{5}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{5}}{2}$

Decimal Form:

$5.59016994 \dots$

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