Evaluate 5/(8- square root of 6)

$\frac{5}{8 - \sqrt{6}}$

Step 1

Multiply $\frac{5}{8 - \sqrt{6}}$ by $\frac{8 + \sqrt{6}}{8 + \sqrt{6}}$ .

$\frac{5}{8 - \sqrt{6}} \cdot \frac{8 + \sqrt{6}}{8 + \sqrt{6}}$

Step 2

Multiply $\frac{5}{8 - \sqrt{6}}$ by $\frac{8 + \sqrt{6}}{8 + \sqrt{6}}$ .

$\frac{5 (8 + \sqrt{6})}{(8 - \sqrt{6}) (8 + \sqrt{6})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (8 + \sqrt{6})}{64 + 8 \sqrt{6} - 8 \sqrt{6} - {\sqrt{6}}^{2}}$

Step 4

Simplify.

$\frac{5 (8 + \sqrt{6})}{58}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (8 + \sqrt{6})}{58}$

Decimal Form:

$0.90081808 \dots$