Algebra Examples

$\frac{1}{3 + \sqrt{2}}$

Step 1

Multiply $\frac{1}{3 + \sqrt{2}}$ by $\frac{3 - \sqrt{2}}{3 - \sqrt{2}}$ .

$\frac{1}{3 + \sqrt{2}} \cdot \frac{3 - \sqrt{2}}{3 - \sqrt{2}}$

Step 2

Multiply $\frac{1}{3 + \sqrt{2}}$ by $\frac{3 - \sqrt{2}}{3 - \sqrt{2}}$ .

$\frac{3 - \sqrt{2}}{(3 + \sqrt{2}) (3 - \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 - \sqrt{2}}{9 - 3 \sqrt{2} + \sqrt{2} \cdot 3 - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{3 - \sqrt{2}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 - \sqrt{2}}{7}$

Decimal Form:

$0.22654091 \dots$