# How do you simplify  (2+ sqrt3)(2- sqrt3) ?

Nov 1, 2015

$\left(2 + \sqrt{3}\right) \left(2 - \sqrt{3}\right) = 1$

#### Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

Putting $a = 2$ and $b = \sqrt{3}$ we find:

$\left(2 + \sqrt{3}\right) \left(2 - \sqrt{3}\right) = {2}^{2} - {\left(\sqrt{3}\right)}^{2} = 4 - 3 = 1$