Evaluate 2/(5- square root of 3)

$\frac{2}{5 - \sqrt{3}}$

Step 1

Multiply $\frac{2}{5 - \sqrt{3}}$ by $\frac{5 + \sqrt{3}}{5 + \sqrt{3}}$ .

$\frac{2}{5 - \sqrt{3}} \cdot \frac{5 + \sqrt{3}}{5 + \sqrt{3}}$

Step 2

Multiply $\frac{2}{5 - \sqrt{3}}$ by $\frac{5 + \sqrt{3}}{5 + \sqrt{3}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{2 (5 + \sqrt{3})}{25 + 5 \sqrt{3} - 5 \sqrt{3} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{2 (5 + \sqrt{3})}{22}$

Step 5

Cancel the common factors.

Factor $2$ out of $22$ .

$\frac{2 (5 + \sqrt{3})}{2 \cdot 11}$

Cancel the common factor.

$\frac{2 (5 + \sqrt{3})}{2 \cdot 11}$

Rewrite the expression.

$\frac{5 + \sqrt{3}}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5 + \sqrt{3}}{11}$

Decimal Form:

$0.61200461 \dots$