Finite Math Examples

$\frac{1}{5 + \sqrt{3}}$

Step 1

Multiply $\frac{1}{5 + \sqrt{3}}$ by $\frac{5 - \sqrt{3}}{5 - \sqrt{3}}$ .

$\frac{1}{5 + \sqrt{3}} \cdot \frac{5 - \sqrt{3}}{5 - \sqrt{3}}$

Step 2

Multiply $\frac{1}{5 + \sqrt{3}}$ by $\frac{5 - \sqrt{3}}{5 - \sqrt{3}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{5 - \sqrt{3}}{25 - 5 \sqrt{3} + \sqrt{3} \cdot 5 - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{5 - \sqrt{3}}{22}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 - \sqrt{3}}{22}$

Decimal Form:

$0.14854314 \dots$