Basic Math Examples

$\frac{\sqrt{52}}{- 8}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite

$52$ as

$2^{2} \cdot 13$ .

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Step 1.1.1

Factor

$4$ out of

$52$ .

$\frac{\sqrt{4 (13)}}{- 8}$

Step 1.1.2

Rewrite

$4$ as

$2^{2}$ .

$\frac{\sqrt{2^{2} \cdot 13}}{- 8}$

$\frac{\sqrt{2^{2} \cdot 13}}{- 8}$

Step 1.2

Pull terms out from under the radical.

$\frac{2 \sqrt{13}}{- 8}$

$\frac{2 \sqrt{13}}{- 8}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of

$2$ and

$- 8$ .

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Step 2.1.1

Factor

$2$ out of

$2 \sqrt{13}$ .

$\frac{2 (\sqrt{13})}{- 8}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor

$2$ out of

$- 8$ .

$\frac{2 \sqrt{13}}{2 \cdot - 4}$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 \sqrt{13}}{2 \cdot - 4}$

Step 2.1.2.3

Rewrite the expression.

$\frac{\sqrt{13}}{- 4}$

$\frac{\sqrt{13}}{- 4}$

$\frac{\sqrt{13}}{- 4}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{\sqrt{13}}{4}$

$- \frac{\sqrt{13}}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{13}}{4}$

Decimal Form:

$- 0.90138781 \dots$

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