Question: prove that 2 minus root 3 is irrational?
Answer: We may assume that 2 is rational because 2 = 2/1 and 2 is prime. So, it is sufficient to prove that sqrt(3) is irrational (because the rationals are closed under multiplication). Let a/b = sqrt(3) where a, b are relatively prime. Then, we can say that a = 3m for some integer.