Utilize theory of equations, specifically rational zeros theorem, to prove that some numbers involving radicals of integers are irrational. Illustrate that number a = sqrt(3) - sqrt(2) is irrational.
1. Determine the integral (coefficient) polynomial for which a is a zero.
2. Use rational zeros theorem to illustrate that the polynomial from 1. above has no rational zeros.
3. Use this method to illustrate that for any positive integer n which is not the perfect square of integer, sqrt(n) is irrational.