Pre-Algebra Examples

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

Step 1

Multiply $\frac{2}{\sqrt{7} + \sqrt{2}}$ by $\frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}}$ .

$\frac{2}{\sqrt{7} + \sqrt{2}} \cdot \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}}$

Step 2

Multiply $\frac{2}{\sqrt{7} + \sqrt{2}}$ by $\frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}}$ .

$\frac{2 (\sqrt{7} - \sqrt{2})}{(\sqrt{7} + \sqrt{2}) (\sqrt{7} - \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{2 (\sqrt{7} - \sqrt{2})}{{\sqrt{7}}^{2} - \sqrt{14} + \sqrt{14} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{2 (\sqrt{7} - \sqrt{2})}{5}$

Step 5

Apply the distributive property.

$\frac{2 \sqrt{7} + 2 (- \sqrt{2})}{5}$

Step 6

Multiply $- 1$ by $2$ .

$\frac{2 \sqrt{7} - 2 \sqrt{2}}{5}$

Step 7

Split the fraction $\frac{2 \sqrt{7} - 2 \sqrt{2}}{5}$ into two fractions.

$\frac{2 \sqrt{7}}{5} + \frac{- 2 \sqrt{2}}{5}$

Step 8

Move the negative in front of the fraction.

$\frac{2 \sqrt{7}}{5} - \frac{2 \sqrt{2}}{5}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{7}}{5} - \frac{2 \sqrt{2}}{5}$

Decimal Form:

$0.49261509 \dots$