Evaluate 8/(8- square root of 7)

$\frac{8}{8 - \sqrt{7}}$

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{8 (8 + \sqrt{7})}{57}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{8 (8 + \sqrt{7})}{57}$

Decimal Form:

$1.49414053 \dots$