Evaluate 5/(2- square root of 7)

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

Step 1

Multiply $\frac{5}{2 - \sqrt{7}}$ by $\frac{2 + \sqrt{7}}{2 + \sqrt{7}}$ .

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

Step 2

Multiply $\frac{5}{2 - \sqrt{7}}$ by $\frac{2 + \sqrt{7}}{2 + \sqrt{7}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (2 + \sqrt{7})}{4 + 2 \sqrt{7} - 2 \sqrt{7} - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{5 (2 + \sqrt{7})}{- 3}$

Step 5

Move the negative in front of the fraction.

$- \frac{5 (2 + \sqrt{7})}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{5 (2 + \sqrt{7})}{3}$

Decimal Form:

$- 7.74291885 \dots$