Evaluate 3/(9- square root of 5)

$\frac{3}{9 - \sqrt{5}}$

Step 1

Multiply $\frac{3}{9 - \sqrt{5}}$ by $\frac{9 + \sqrt{5}}{9 + \sqrt{5}}$ .

$\frac{3}{9 - \sqrt{5}} \cdot \frac{9 + \sqrt{5}}{9 + \sqrt{5}}$

Step 2

Multiply $\frac{3}{9 - \sqrt{5}}$ by $\frac{9 + \sqrt{5}}{9 + \sqrt{5}}$ .

$\frac{3 (9 + \sqrt{5})}{(9 - \sqrt{5}) (9 + \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (9 + \sqrt{5})}{81 + 9 \sqrt{5} - 9 \sqrt{5} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{3 (9 + \sqrt{5})}{76}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (9 + \sqrt{5})}{76}$

Decimal Form:

$0.44352899 \dots$