Simplify 5/( square root of 11- square root of 3)

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

Step 1

Multiply $\frac{5}{\sqrt{11} - \sqrt{3}}$ by $\frac{\sqrt{11} + \sqrt{3}}{\sqrt{11} + \sqrt{3}}$ .

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

Step 2

Multiply $\frac{5}{\sqrt{11} - \sqrt{3}}$ by $\frac{\sqrt{11} + \sqrt{3}}{\sqrt{11} + \sqrt{3}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (\sqrt{11} + \sqrt{3})}{{\sqrt{11}}^{2} + \sqrt{33} - \sqrt{33} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{5 (\sqrt{11} + \sqrt{3})}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (\sqrt{11} + \sqrt{3})}{8}$

Decimal Form:

$3.15542224 \dots$