Question

How do you combine `sqrt 3 - 2`?

Answer 1

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 `(sqrt(3)-2)` by `(sqrt(3)+2)` to get `-1`.

For example, to simplify a rational expression like:

`(5-2sqrt(3))/(sqrt(3)-2)`

by multiplying both the numerator and denominator by the conjugate `sqrt(3)+2` of the denominator, thus:

`(5-2sqrt(3))/(sqrt(3)-2)=((5-2sqrt(3))(sqrt(3)+2))/((sqrt(3)-2)(sqrt(3)+2))`

`=((10-6)+(5-4)sqrt(3))/(sqrt(3)^2-2^2)`

`=(4+sqrt(3))/(3-4) = (4+sqrt(3))/-1 = -4-sqrt(3)`