Divide 2/( square root of 13+ square root of 11)

$\frac{2}{\sqrt{13} + \sqrt{11}}$

Step 1

Multiply $\frac{2}{\sqrt{13} + \sqrt{11}}$ by $\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$ .

$\frac{2}{\sqrt{13} + \sqrt{11}} \cdot \frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$

Step 2

Multiply $\frac{2}{\sqrt{13} + \sqrt{11}}$ by $\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} - \sqrt{11}}$ .

$\frac{2 (\sqrt{13} - \sqrt{11})}{(\sqrt{13} + \sqrt{11}) (\sqrt{13} - \sqrt{11})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{2 (\sqrt{13} - \sqrt{11})}{{\sqrt{13}}^{2} - \sqrt{143} + \sqrt{143} - {\sqrt{11}}^{2}}$

Step 4

Simplify.

$\frac{2 (\sqrt{13} - \sqrt{11})}{2}$

Step 5

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (\sqrt{13} - \sqrt{11})}{2}$

Divide $\sqrt{13} - \sqrt{11}$ by $1$ .

$\sqrt{13} - \sqrt{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{13} - \sqrt{11}$

Decimal Form:

$0.28892648 \dots$