Evaluate 2/(4- square root of 5)

$\frac{2}{4 - \sqrt{5}}$

Step 1

Multiply $\frac{2}{4 - \sqrt{5}}$ by $\frac{4 + \sqrt{5}}{4 + \sqrt{5}}$ .

$\frac{2}{4 - \sqrt{5}} \cdot \frac{4 + \sqrt{5}}{4 + \sqrt{5}}$

Step 2

Multiply $\frac{2}{4 - \sqrt{5}}$ by $\frac{4 + \sqrt{5}}{4 + \sqrt{5}}$ .

$\frac{2 (4 + \sqrt{5})}{(4 - \sqrt{5}) (4 + \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{2 (4 + \sqrt{5})}{16 + 4 \sqrt{5} - 4 \sqrt{5} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{2 (4 + \sqrt{5})}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 (4 + \sqrt{5})}{11}$

Decimal Form:

$1.13383054 \dots$