# How do you simplify (6+ square root 3)(6-square root 3)?

Jul 20, 2015

$\left(6 + \sqrt{3}\right) \cdot \left(6 - \sqrt{3}\right) = {6}^{2} - {\left(\sqrt{3}\right)}^{2} = 36 - 3 = 33$

#### Explanation:

General property this problem is based upon is
$\left(a + b\right) \cdot \left(a - b\right) = {a}^{2} - {b}^{2}$

Indeed, if we open the parenthesis in the original expression, we get:
$\left(a + b\right) \cdot \left(a - b\right) = a \cdot a + b \cdot a - a \cdot b - b \cdot b = {a}^{2} - {b}^{2}$

Using the above property for $a = 6$ and $b = \sqrt{3}$, we obtain
$\left(6 + \sqrt{3}\right) \cdot \left(6 - \sqrt{3}\right) = {6}^{2} - {\left(\sqrt{3}\right)}^{2} = 36 - 3 = 33$

So, $33$ is the final answer.