Algebra Examples

$5 \div (3 + \sqrt{5})$

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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

Step 3

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

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

Step 4

Expand the denominator using the FOIL method.

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

Step 5

Simplify.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.95491502 \dots$