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

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

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

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

Simplify the expression.

Move the negative one from the denominator of $\frac{\sqrt{3} + \sqrt{5}}{- 1}$ .

$- 1 \cdot (\sqrt{3} + \sqrt{5})$

Rewrite $- 1 \cdot (\sqrt{3} + \sqrt{5})$ as $- (\sqrt{3} + \sqrt{5})$ .

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

Apply the distributive property.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 3.96811878 \dots$