Algebra Examples

$\frac{3}{5 - \sqrt{2}}$

Step 1

Multiply $\frac{3}{5 - \sqrt{2}}$ by $\frac{5 + \sqrt{2}}{5 + \sqrt{2}}$ .

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

Step 2

Multiply $\frac{3}{5 - \sqrt{2}}$ by $\frac{5 + \sqrt{2}}{5 + \sqrt{2}}$ .

$\frac{3 (5 + \sqrt{2})}{(5 - \sqrt{2}) (5 + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{3 (5 + \sqrt{2})}{23}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (5 + \sqrt{2})}{23}$

Decimal Form:

$0.83663655 \dots$