Simplify 1/( square root of 3+2)

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

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

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

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

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

Expand the denominator using the FOIL method.

$\frac{\sqrt{3} - 2}{{\sqrt{3}}^{2} + \sqrt{3} \cdot - 2 + 2 \sqrt{3} - 4}$

Simplify.

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

Simplify the expression.

Move the negative one from the denominator of $\frac{\sqrt{3} - 2}{- 1}$ .

$- 1 \cdot (\sqrt{3} - 2)$

Rewrite $- 1 \cdot (\sqrt{3} - 2)$ as $- (\sqrt{3} - 2)$ .

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

Apply the distributive property.

$- \sqrt{3} - - 2$

Multiply $- 1$ by $- 2$ .

$- \sqrt{3} + 2$

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{3} + 2$

Decimal Form:

$0.26794919 \dots$