Simplify 2/( square root of 7- square root of 5)

$\frac{2}{\sqrt{7} - \sqrt{5}}$

Step 1

Multiply $\frac{2}{\sqrt{7} - \sqrt{5}}$ by $\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}$ .

$\frac{2}{\sqrt{7} - \sqrt{5}} \cdot \frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}$

Step 2

Multiply $\frac{2}{\sqrt{7} - \sqrt{5}}$ by $\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}$ .

$\frac{2 (\sqrt{7} + \sqrt{5})}{(\sqrt{7} - \sqrt{5}) (\sqrt{7} + \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{2 (\sqrt{7} + \sqrt{5})}{{\sqrt{7}}^{2} + \sqrt{35} - \sqrt{35} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{2 (\sqrt{7} + \sqrt{5})}{2}$

Step 5

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (\sqrt{7} + \sqrt{5})}{2}$

Divide $\sqrt{7} + \sqrt{5}$ by $1$ .

$\sqrt{7} + \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{7} + \sqrt{5}$

Decimal Form:

$4.88181928 \dots$