Basic Math Examples

$\frac{11}{7 + \sqrt{11}}$

Step 1

Multiply $\frac{11}{7 + \sqrt{11}}$ by $\frac{7 - \sqrt{11}}{7 - \sqrt{11}}$ .

$\frac{11}{7 + \sqrt{11}} \cdot \frac{7 - \sqrt{11}}{7 - \sqrt{11}}$

Step 2

Multiply $\frac{11}{7 + \sqrt{11}}$ by $\frac{7 - \sqrt{11}}{7 - \sqrt{11}}$ .

$\frac{11 (7 - \sqrt{11})}{(7 + \sqrt{11}) (7 - \sqrt{11})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{11 (7 - \sqrt{11})}{49 - 7 \sqrt{11} + \sqrt{11} \cdot 7 - {\sqrt{11}}^{2}}$

Step 4

Simplify.

$\frac{11 (7 - \sqrt{11})}{38}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{11 (7 - \sqrt{11})}{38}$

Decimal Form:

$1.06624019 \dots$