1. The problem statement, all variables and given/known data Prove that x = 2^(1/2)+2^(1/3) is irrational. 2. Relevant equations 3. The attempt at a solution The hint to the exercise says that I should first show that x satisfies an equation of the form x^6+a_1*X^5+...+a_0 = 0, where the coefficients are integers. I am having trouble showing that x satisfies such an equation. I tried multiplying (x-2^(1/2)-2^(1/3))(x+2^(1/2)-2^(1/3)) but was not successful in getting integer coefficients.