Evaluate 1/(5- square root of 7)

$\frac{1}{5 - \sqrt{7}}$

Step 1

Multiply $\frac{1}{5 - \sqrt{7}}$ by $\frac{5 + \sqrt{7}}{5 + \sqrt{7}}$ .

$\frac{1}{5 - \sqrt{7}} \cdot \frac{5 + \sqrt{7}}{5 + \sqrt{7}}$

Step 2

Multiply $\frac{1}{5 - \sqrt{7}}$ by $\frac{5 + \sqrt{7}}{5 + \sqrt{7}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{5 + \sqrt{7}}{25 + 5 \sqrt{7} - 5 \sqrt{7} - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{5 + \sqrt{7}}{18}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 + \sqrt{7}}{18}$

Decimal Form:

$0.42476396 \dots$