Evaluate 3/(9- square root of 2)

$\frac{3}{9 - \sqrt{2}}$

Step 1

Multiply $\frac{3}{9 - \sqrt{2}}$ by $\frac{9 + \sqrt{2}}{9 + \sqrt{2}}$ .

$\frac{3}{9 - \sqrt{2}} \cdot \frac{9 + \sqrt{2}}{9 + \sqrt{2}}$

Step 2

Multiply $\frac{3}{9 - \sqrt{2}}$ by $\frac{9 + \sqrt{2}}{9 + \sqrt{2}}$ .

$\frac{3 (9 + \sqrt{2})}{(9 - \sqrt{2}) (9 + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (9 + \sqrt{2})}{81 + 9 \sqrt{2} - 9 \sqrt{2} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{3 (9 + \sqrt{2})}{79}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (9 + \sqrt{2})}{79}$

Decimal Form:

$0.39547646 \dots$