Prove that $\sqrt 2 + \sqrt 6$ is irrational. (Note that, in general, the sum of two irrational numbers could be rational.)
I tried attempting to use proof by contradiction but I'm unsure of how to go from even there. I have no clue other than that. Please help.
Best Answer
If it is rational, its square is also rational. But this would imply that $\sqrt{3}$ is rational.