Simplify 6/(3- square root of 5)

$\frac{6}{3 - \sqrt{5}}$

Multiply $\frac{6}{3 - \sqrt{5}}$ by $\frac{3 + \sqrt{5}}{3 + \sqrt{5}}$ .

$\frac{6}{3 - \sqrt{5}} \cdot \frac{3 + \sqrt{5}}{3 + \sqrt{5}}$

Multiply $\frac{6}{3 - \sqrt{5}}$ by $\frac{3 + \sqrt{5}}{3 + \sqrt{5}}$ .

$\frac{6 (3 + \sqrt{5})}{(3 - \sqrt{5}) (3 + \sqrt{5})}$

Expand the denominator using the FOIL method.

$\frac{6 (3 + \sqrt{5})}{9 + 3 \sqrt{5} - 3 \sqrt{5} - {\sqrt{5}}^{2}}$

Simplify.

$\frac{6 (3 + \sqrt{5})}{4}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6 (3 + \sqrt{5})$ .

$\frac{2 (3 (3 + \sqrt{5}))}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 (3 (3 + \sqrt{5}))}{2 (2)}$

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 (3 + \sqrt{5})}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (3 + \sqrt{5})}{2}$

Decimal Form:

$7.85410196 \dots$