1. The problem statement, all variables and given/known data Number Theory homework. I'm supposed to prove that the value 2^.5 + 3^.5 is irrational by finding a monic polynomial that the aforementioned number is a root of. This would be trivial if I were supposed to prove that just 2^.5 was irrational because its monic polynomial equation would be x^2 -2 = 0. But I can't just raise 2^.5 + 3^.5 to a power and then subtract it to get my desired polynomial because all coefficients of a monic polynomial have to be integers, and 2^.5 + 3^.5 is obviously not an integer. What method should I use to go about finding such a monic polynomial?