Evaluate 9/(1+ square root of 5)

$\frac{9}{1 + \sqrt{5}}$

Step 1

Multiply $\frac{9}{1 + \sqrt{5}}$ by $\frac{1 - \sqrt{5}}{1 - \sqrt{5}}$ .

$\frac{9}{1 + \sqrt{5}} \cdot \frac{1 - \sqrt{5}}{1 - \sqrt{5}}$

Step 2

Multiply $\frac{9}{1 + \sqrt{5}}$ by $\frac{1 - \sqrt{5}}{1 - \sqrt{5}}$ .

$\frac{9 (1 - \sqrt{5})}{(1 + \sqrt{5}) (1 - \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{9 (1 - \sqrt{5})}{1 - \sqrt{5} + \sqrt{5} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{9 (1 - \sqrt{5})}{- 4}$

Step 5

Move the negative in front of the fraction.

$- \frac{9 (1 - \sqrt{5})}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{9 (1 - \sqrt{5})}{4}$

Decimal Form:

$2.78115294 \dots$