Trigonometry Examples

$\frac{1}{7 - \sqrt{11}}$

Step 1

Multiply $\frac{1}{7 - \sqrt{11}}$ by $\frac{7 + \sqrt{11}}{7 + \sqrt{11}}$ .

$\frac{1}{7 - \sqrt{11}} \cdot \frac{7 + \sqrt{11}}{7 + \sqrt{11}}$

Step 2

Multiply $\frac{1}{7 - \sqrt{11}}$ by $\frac{7 + \sqrt{11}}{7 + \sqrt{11}}$ .

$\frac{7 + \sqrt{11}}{(7 - \sqrt{11}) (7 + \sqrt{11})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 + \sqrt{11}}{49 + 7 \sqrt{11} - 7 \sqrt{11} - {\sqrt{11}}^{2}}$

Step 4

Simplify.

$\frac{7 + \sqrt{11}}{38}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7 + \sqrt{11}}{38}$

Decimal Form:

$0.27149012 \dots$