How do you combine sqrt 3 - 2?

Nov 8, 2015

You cannot simplify this expression.

However, if you need to rationalize it out of a denominator, you can multiply by its conjugate $\sqrt{3} + 2$ to get $- 1$

Explanation:

You cannot combine $\sqrt{3}$ and $- 2$ in a simple way, but you can multiply $\left(\sqrt{3} - 2\right)$ by $\left(\sqrt{3} + 2\right)$ to get $- 1$.

For example, to simplify a rational expression like:

$\frac{5 - 2 \sqrt{3}}{\sqrt{3} - 2}$

by multiplying both the numerator and denominator by the conjugate $\sqrt{3} + 2$ of the denominator, thus:

$\frac{5 - 2 \sqrt{3}}{\sqrt{3} - 2} = \frac{\left(5 - 2 \sqrt{3}\right) \left(\sqrt{3} + 2\right)}{\left(\sqrt{3} - 2\right) \left(\sqrt{3} + 2\right)}$

$= \frac{\left(10 - 6\right) + \left(5 - 4\right) \sqrt{3}}{{\sqrt{3}}^{2} - {2}^{2}}$

$= \frac{4 + \sqrt{3}}{3 - 4} = \frac{4 + \sqrt{3}}{-} 1 = - 4 - \sqrt{3}$