Basic Math Examples

$\frac{- 3 - \sqrt{75}}{30}$

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 $75$ .

$\frac{- 3 - \sqrt{25 (3)}}{30}$

Step 1.1.2

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

$\frac{- 3 - \sqrt{5^{2} \cdot 3}}{30}$

$\frac{- 3 - \sqrt{5^{2} \cdot 3}}{30}$

Step 1.2

Pull terms out from under the radical.

$\frac{- 3 - (5 \sqrt{3})}{30}$

Step 1.3

Multiply $5$ by $- 1$ .

$\frac{- 3 - 5 \sqrt{3}}{30}$

$\frac{- 3 - 5 \sqrt{3}}{30}$

Step 2

Simplify with factoring out.

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Step 2.1

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- 1 (3) - 5 \sqrt{3}}{30}$

Step 2.2

Factor $- 1$ out of $- 5 \sqrt{3}$ .

$\frac{- 1 (3) - (5 \sqrt{3})}{30}$

Step 2.3

Factor $- 1$ out of $- 1 (3) - (5 \sqrt{3})$ .

$\frac{- 1 (3 + 5 \sqrt{3})}{30}$

Step 2.4

Move the negative in front of the fraction.

$- \frac{3 + 5 \sqrt{3}}{30}$

$- \frac{3 + 5 \sqrt{3}}{30}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 + 5 \sqrt{3}}{30}$

Decimal Form:

$- 0.38867513 \dots$

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