Simplify the Radical Expression 1/(1+ square root of 3)

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

Step 1

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

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

Step 2

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

$\frac{1 - \sqrt{3}}{(1 + \sqrt{3}) (1 - \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.36602540 \dots$