Simplify (3a)/( square root of 9+ square root of 5)

$\frac{3 a}{\sqrt{9} + \sqrt{5}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$\frac{3 a}{\sqrt{3^{2}} + \sqrt{5}}$

Pull terms out from under the radical, assuming positive real numbers.

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

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

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