Pre-Algebra Examples

$\frac{4}{3 - \sqrt{2}}$

Step 1

Multiply $\frac{4}{3 - \sqrt{2}}$ by $\frac{3 + \sqrt{2}}{3 + \sqrt{2}}$ .

$\frac{4}{3 - \sqrt{2}} \cdot \frac{3 + \sqrt{2}}{3 + \sqrt{2}}$

Step 2

Multiply $\frac{4}{3 - \sqrt{2}}$ by $\frac{3 + \sqrt{2}}{3 + \sqrt{2}}$ .

$\frac{4 (3 + \sqrt{2})}{(3 - \sqrt{2}) (3 + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (3 + \sqrt{2})}{9 + 3 \sqrt{2} - 3 \sqrt{2} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{4 (3 + \sqrt{2})}{7}$

Step 5

Apply the distributive property.

$\frac{4 \cdot 3 + 4 \sqrt{2}}{7}$

Step 6

Multiply $4$ by $3$ .

$\frac{12 + 4 \sqrt{2}}{7}$

Step 7

Split the fraction $\frac{12 + 4 \sqrt{2}}{7}$ into two fractions.

$\frac{12}{7} + \frac{4 \sqrt{2}}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{7} + \frac{4 \sqrt{2}}{7}$

Decimal Form:

$2.52240774 \dots$