Simplify 2/( square root of 5- square root of 3)

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

$\frac{2 (\sqrt{5} + \sqrt{3})}{{\sqrt{5}}^{2} + \sqrt{15} - \sqrt{15} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

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

Step 5

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $\sqrt{5} + \sqrt{3}$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.96811878 \dots$