Evaluate 4/(8- square root of 3)

$\frac{4}{8 - \sqrt{3}}$

Step 1

Multiply $\frac{4}{8 - \sqrt{3}}$ by $\frac{8 + \sqrt{3}}{8 + \sqrt{3}}$ .

$\frac{4}{8 - \sqrt{3}} \cdot \frac{8 + \sqrt{3}}{8 + \sqrt{3}}$

Step 2

Multiply $\frac{4}{8 - \sqrt{3}}$ by $\frac{8 + \sqrt{3}}{8 + \sqrt{3}}$ .

$\frac{4 (8 + \sqrt{3})}{(8 - \sqrt{3}) (8 + \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (8 + \sqrt{3})}{64 + 8 \sqrt{3} - 8 \sqrt{3} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{4 (8 + \sqrt{3})}{61}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (8 + \sqrt{3})}{61}$

Decimal Form:

$0.63816726 \dots$