Use the rational root theorem.
I do not even know where to start with this. this proof is for an abstract algebra course.
Suppose f(x) = xn + a1xn-1 + . . . + a1x + a0 where the coefficients a0,a1, . . . ,an-1 are integers.
prove: if f(b) = 0 and b is not an integer, then b is irrational.