Simplify 2/(1- square root of 3)

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

Step 1

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

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

Step 2

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

$\frac{2 (1 + \sqrt{3})}{(1 - \sqrt{3}) (1 + \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{2 (1 + \sqrt{3})}{- 2}$

Step 5

Simplify the expression.

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

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

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

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

Step 6

Apply the distributive property.

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

Step 7

Multiply $- 1$ by $1$ .

$- 1 - \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 1 - \sqrt{3}$

Decimal Form:

$- 2.73205080 \dots$