Simplify 1/( square root of 3+ square root of 2)

$\frac{1}{\sqrt{3} + \sqrt{2}}$

Step 1

Multiply $\frac{1}{\sqrt{3} + \sqrt{2}}$ by $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ .

$\frac{1}{\sqrt{3} + \sqrt{2}} \cdot \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}$

Step 2

Multiply $\frac{1}{\sqrt{3} + \sqrt{2}}$ by $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{\sqrt{3} - \sqrt{2}}{{\sqrt{3}}^{2} - \sqrt{6} + \sqrt{6} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{\sqrt{3} - \sqrt{2}}{1}$

Step 5

Divide $\sqrt{3} - \sqrt{2}$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.31783724 \dots$