Simplify 8/(3- square root of 5)

$\frac{8}{3 - \sqrt{5}}$

Multiply $\frac{8}{3 - \sqrt{5}}$ by $\frac{3 + \sqrt{5}}{3 + \sqrt{5}}$ .

$\frac{8}{3 - \sqrt{5}} \cdot \frac{3 + \sqrt{5}}{3 + \sqrt{5}}$

Multiply $\frac{8}{3 - \sqrt{5}}$ by $\frac{3 + \sqrt{5}}{3 + \sqrt{5}}$ .

$\frac{8 (3 + \sqrt{5})}{(3 - \sqrt{5}) (3 + \sqrt{5})}$

Expand the denominator using the FOIL method.

$\frac{8 (3 + \sqrt{5})}{9 + 3 \sqrt{5} - 3 \sqrt{5} - {\sqrt{5}}^{2}}$

Simplify.

$\frac{8 (3 + \sqrt{5})}{4}$

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 (3 + \sqrt{5})$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (2 (3 + \sqrt{5}))}{4 (1)}$

Cancel the common factor.

$\frac{4 (2 (3 + \sqrt{5}))}{4 \cdot 1}$

Rewrite the expression.

$\frac{2 (3 + \sqrt{5})}{1}$

Divide $2 (3 + \sqrt{5})$ by $1$ .

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

Apply the distributive property.

$2 \cdot 3 + 2 \sqrt{5}$

Multiply $2$ by $3$ .

$6 + 2 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$6 + 2 \sqrt{5}$

Decimal Form:

$10.47213595 \dots$