Thread: Proving the irrationality of the sum of non perfect square roots?

I know how to prove that the is irrational, and that is irrational. But how does one go about using the tricks involved in the proof on something like proving that is irrational if:



?

Thanks in advance

You can prove this by contradiction. Assume P is rational.

then try squaring the equation



Use the facts that a square of a rational is a rational, and rational number addition and scalar multiplication is closed under the rational field.

Fiddle around with the squared equation and you'll just have to prove is irrational using those tricks you mentioned, which leads to a contradiction (a rational number = an irrational number)

If I'm not missing something you have posted this before, and it has received a considerable attention in here.

My bad, yes I must've posted it before. I had thought it was different problem. I wasn't sure. Wont happen again

Oh, and thanks for the help Gusbob, I figured out the polynomial that represented the squared version and had no trouble proving the irrationality of 6^(1/2). That was a clever idea to use the square of the sum of the square roots. I hadn't thought of that before, I know I used it once along time ago, but I forgot about it. Thanks for the help.