Basic Math Examples

$\frac{- 10 + \sqrt{75}}{10}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.1.1

Factor $25$ out of $75$ .

$\frac{- 10 + \sqrt{25 (3)}}{10}$

Step 1.1.2

Rewrite $25$ as $5^{2}$ .

$\frac{- 10 + \sqrt{5^{2} \cdot 3}}{10}$

$\frac{- 10 + \sqrt{5^{2} \cdot 3}}{10}$

Step 1.2

Pull terms out from under the radical.

$\frac{- 10 + 5 \sqrt{3}}{10}$

$\frac{- 10 + 5 \sqrt{3}}{10}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $- 10 + 5 \sqrt{3}$ and $10$ .

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Step 2.1.1

Factor $5$ out of $- 10$ .

$\frac{5 \cdot - 2 + 5 \sqrt{3}}{10}$

Step 2.1.2

Factor $5$ out of $5 \sqrt{3}$ .

$\frac{5 \cdot - 2 + 5 (\sqrt{3})}{10}$

Step 2.1.3

Factor $5$ out of $5 \cdot - 2 + 5 (\sqrt{3})$ .

$\frac{5 \cdot (- 2 + \sqrt{3})}{10}$

Step 2.1.4

Cancel the common factors.

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Step 2.1.4.1

Factor $5$ out of $10$ .

$\frac{5 \cdot (- 2 + \sqrt{3})}{5 (2)}$

Step 2.1.4.2

Cancel the common factor.

$\frac{5 \cdot (- 2 + \sqrt{3})}{5 \cdot 2}$

Step 2.1.4.3

Rewrite the expression.

$\frac{- 2 + \sqrt{3}}{2}$

$\frac{- 2 + \sqrt{3}}{2}$

$\frac{- 2 + \sqrt{3}}{2}$

Step 2.2

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- 1 (2) + \sqrt{3}}{2}$

Step 2.3

Factor $- 1$ out of $\sqrt{3}$ .

$\frac{- 1 (2) - 1 (- \sqrt{3})}{2}$

Step 2.4

Factor $- 1$ out of $- 1 (2) - 1 (- \sqrt{3})$ .

$\frac{- 1 (2 - \sqrt{3})}{2}$

Step 2.5

Move the negative in front of the fraction.

$- \frac{2 - \sqrt{3}}{2}$

$- \frac{2 - \sqrt{3}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 - \sqrt{3}}{2}$

Decimal Form:

$- 0.13397459 \dots$

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