Basic Math Examples

$\frac{5}{8 + \sqrt{7}}$

Step 1

Multiply $\frac{5}{8 + \sqrt{7}}$ by $\frac{8 - \sqrt{7}}{8 - \sqrt{7}}$ .

$\frac{5}{8 + \sqrt{7}} \cdot \frac{8 - \sqrt{7}}{8 - \sqrt{7}}$

Step 2

Multiply $\frac{5}{8 + \sqrt{7}}$ by $\frac{8 - \sqrt{7}}{8 - \sqrt{7}}$ .

$\frac{5 (8 - \sqrt{7})}{(8 + \sqrt{7}) (8 - \sqrt{7})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (8 - \sqrt{7})}{64 - 8 \sqrt{7} + \sqrt{7} \cdot 8 - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{5 (8 - \sqrt{7})}{57}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (8 - \sqrt{7})}{57}$

Decimal Form:

$0.46967093 \dots$