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## Main Question or Discussion Point

I want to prove 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.

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.

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