Evaluate 2/(9- square root of 10)

$\frac{2}{9 - \sqrt{10}}$

Step 1

Multiply $\frac{2}{9 - \sqrt{10}}$ by $\frac{9 + \sqrt{10}}{9 + \sqrt{10}}$ .

$\frac{2}{9 - \sqrt{10}} \cdot \frac{9 + \sqrt{10}}{9 + \sqrt{10}}$

Step 2

Multiply $\frac{2}{9 - \sqrt{10}}$ by $\frac{9 + \sqrt{10}}{9 + \sqrt{10}}$ .

$\frac{2 (9 + \sqrt{10})}{(9 - \sqrt{10}) (9 + \sqrt{10})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{2 (9 + \sqrt{10})}{81 + 9 \sqrt{10} - 9 \sqrt{10} - {\sqrt{10}}^{2}}$

Step 4

Simplify.

$\frac{2 (9 + \sqrt{10})}{71}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 (9 + \sqrt{10})}{71}$

Decimal Form:

$0.34259937 \dots$