# How do you simplify sqrt3 - 2sqrt3?

Sep 4, 2015

=color(blue)(-9

#### Explanation:

$\sqrt{3} - 2 \sqrt{3}$ can be simplified by multiplying the expression by its the conjugate which =color(blue)(sqrt3 +2sqrt3

=$\left(\sqrt{3} - 2 \sqrt{3}\right) \cdot \left(\textcolor{b l u e}{\sqrt{3} + 2 \sqrt{3}}\right)$

Now, we can apply the property :
(a-b)(a+b) = color(blue)(a^2-b^2

$\left(\sqrt{3} - 2 \sqrt{3}\right) \cdot \left(\textcolor{b l u e}{\sqrt{3} + 2 \sqrt{3}}\right) = {\left(\sqrt{3}\right)}^{2} - {\left(2 \sqrt{3}\right)}^{2}$
$= 3 - 4 \cdot 3$
$= 3 - 12$
=color(blue)(-9