Is [itex]\mahtbb{Q}(\sqrt{2}, \sqrt{3})[/itex] Galois over Q? If so, something is rational if and only if it is equal to all of its conjugates. (The same is true if the field isn't galois... it's just that in that case, its conjugates would live in other fields)I want to proof that [tex]\sqrt 6 - \sqrt 2- \sqrt 3[/tex] is irrational.
I already know that [tex]\sqrt 2+\sqrt 3[/tex] is irrational (by squaring it). I would like a proof that doesn't use a polynomial and the rational root theorem.
Thanks.
Hi abruzzi!II already know that [tex]\sqrt 2+\sqrt 3[/tex] is irrational (by squaring it).