Basic Math Examples

\frac{45 - 65}{\sqrt{10}}

$\frac{45 - 65}{\sqrt{10}}$

Step 1

Subtract

65

$65$ from

45

$45$ .

\frac{- 20}{\sqrt{10}}

$\frac{- 20}{\sqrt{10}}$

Step 2

Move the negative in front of the fraction.

- \frac{20}{\sqrt{10}}

$- \frac{20}{\sqrt{10}}$

Step 3

Multiply

\frac{20}{\sqrt{10}}

$\frac{20}{\sqrt{10}}$ by

\frac{\sqrt{10}}{\sqrt{10}}

$\frac{\sqrt{10}}{\sqrt{10}}$ .

- (\frac{20}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}})

$- (\frac{20}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}})$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply

\frac{20}{\sqrt{10}}

$\frac{20}{\sqrt{10}}$ by

\frac{\sqrt{10}}{\sqrt{10}}

$\frac{\sqrt{10}}{\sqrt{10}}$ .

- \frac{20 \sqrt{10}}{\sqrt{10} \sqrt{10}}

$- \frac{20 \sqrt{10}}{\sqrt{10} \sqrt{10}}$

Step 4.2

Raise

\sqrt{10}

$\sqrt{10}$ to the power of

1

$1$ .

- \frac{20 \sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}

$- \frac{20 \sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

Step 4.3

Raise

\sqrt{10}

$\sqrt{10}$ to the power of

1

$1$ .

- \frac{20 \sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}

$- \frac{20 \sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

Step 4.4

Use the power rule

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

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

- \frac{20 \sqrt{10}}{{\sqrt{10}}^{1 + 1}}

$- \frac{20 \sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Step 4.5

Add

1

$1$ and

1

$1$ .

- \frac{20 \sqrt{10}}{{\sqrt{10}}^{2}}

$- \frac{20 \sqrt{10}}{{\sqrt{10}}^{2}}$

Step 4.6

Rewrite

{\sqrt{10}}^{2}

${\sqrt{10}}^{2}$ as

10

$10$ .

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Step 4.6.1

Use

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

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

\sqrt{10}

$\sqrt{10}$ as

10^{\frac{1}{2}}

$10^{\frac{1}{2}}$ .

- \frac{20 \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}

$- \frac{20 \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

Step 4.6.2

Apply the power rule and multiply exponents,

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

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

- \frac{20 \sqrt{10}}{10^{\frac{1}{2} \cdot 2}}

$- \frac{20 \sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

$2$ .

$- \frac{20 \sqrt{10}}{10^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of

$2$ .

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Step 4.6.4.1

Cancel the common factor.

$- \frac{20 \sqrt{10}}{10^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$- \frac{20 \sqrt{10}}{10^{1}}$

$- \frac{20 \sqrt{10}}{10^{1}}$

Step 4.6.5

Evaluate the exponent.

$- \frac{20 \sqrt{10}}{10}$

$- \frac{20 \sqrt{10}}{10}$

$- \frac{20 \sqrt{10}}{10}$

Step 5

Cancel the common factor of

$20$ and

$10$ .

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Step 5.1

Factor

$10$ out of

$20 \sqrt{10}$ .

$- \frac{10 (2 \sqrt{10})}{10}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

$10$ out of

$10$ .

$- \frac{10 (2 \sqrt{10})}{10 (1)}$

Step 5.2.2

Cancel the common factor.

$- \frac{10 (2 \sqrt{10})}{10 \cdot 1}$

Step 5.2.3

Rewrite the expression.

$- \frac{2 \sqrt{10}}{1}$

Step 5.2.4

Divide

$2 \sqrt{10}$ by

$1$ .

$- (2 \sqrt{10})$

$- (2 \sqrt{10})$

$- (2 \sqrt{10})$

Step 6

Multiply

$2$ by

$- 1$ .

$- 2 \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{10}$

Decimal Form:

$- 6.32455532 \dots$

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