Simplify 3/( square root of 5- square root of 2)

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

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.65028153 \dots$