Trigonometry Examples

$\frac{1}{5 - \sqrt{13}}$

Step 1

Multiply $\frac{1}{5 - \sqrt{13}}$ by $\frac{5 + \sqrt{13}}{5 + \sqrt{13}}$ .

$\frac{1}{5 - \sqrt{13}} \cdot \frac{5 + \sqrt{13}}{5 + \sqrt{13}}$

Step 2

Multiply $\frac{1}{5 - \sqrt{13}}$ by $\frac{5 + \sqrt{13}}{5 + \sqrt{13}}$ .

$\frac{5 + \sqrt{13}}{(5 - \sqrt{13}) (5 + \sqrt{13})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 + \sqrt{13}}{25 + 5 \sqrt{13} - 5 \sqrt{13} - {\sqrt{13}}^{2}}$

Step 4

Simplify.

$\frac{5 + \sqrt{13}}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 + \sqrt{13}}{12}$

Decimal Form:

$0.71712927 \dots$