I want to prove that: $$\sqrt6 - \sqrt2 - \sqrt3$$ is irrational. I have tried using squares, the $p/q$ definition of rationality and the facts that

1)rational$\times$ irrational=irrational (unless rational=0),

2)rational$+$irrational=irrational.

However, I haven't been able to reach some conclusion. Things seem harder than when you have two square roots. Any help would be appreciated!