Evaluate 3/(4+ square root of 5)

$\frac{3}{4 + \sqrt{5}}$

Step 1

Multiply $\frac{3}{4 + \sqrt{5}}$ by $\frac{4 - \sqrt{5}}{4 - \sqrt{5}}$ .

$\frac{3}{4 + \sqrt{5}} \cdot \frac{4 - \sqrt{5}}{4 - \sqrt{5}}$

Step 2

Multiply $\frac{3}{4 + \sqrt{5}}$ by $\frac{4 - \sqrt{5}}{4 - \sqrt{5}}$ .

$\frac{3 (4 - \sqrt{5})}{(4 + \sqrt{5}) (4 - \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (4 - \sqrt{5})}{16 - 4 \sqrt{5} + \sqrt{5} \cdot 4 - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{3 (4 - \sqrt{5})}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (4 - \sqrt{5})}{11}$

Decimal Form:

$0.48107236 \dots$