Simplify 3/( square root of 8+ square root of 5)

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

Simplify the denominator.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

Rewrite $4$ as $2^{2}$ .

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

Pull terms out from under the radical.

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

Multiply $\frac{3}{2 \sqrt{2} + \sqrt{5}}$ by $\frac{2 \sqrt{2} - \sqrt{5}}{2 \sqrt{2} - \sqrt{5}}$ .

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

Multiply $\frac{3}{2 \sqrt{2} + \sqrt{5}}$ by $\frac{2 \sqrt{2} - \sqrt{5}}{2 \sqrt{2} - \sqrt{5}}$ .

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

Expand the denominator using the FOIL method.

$\frac{3 (2 \sqrt{2} - \sqrt{5})}{4 {\sqrt{2}}^{2} - 2 \sqrt{10} + 2 \sqrt{10} - {\sqrt{5}}^{2}}$

Simplify.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $2 \sqrt{2} - \sqrt{5}$ by $1$ .

$2 \sqrt{2} - \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2} - \sqrt{5}$

Decimal Form:

$0.59235914 \dots$