I need to show that a rational + irrational number is irrational. I am trying to do a proof by contradiction. So far I have: Suppose a rational, b irrational. Then a = p/q for p, q in Z. Then a + b = p/q + b = (p + qb) / q But I don't know where to go from here because I still have a rational plus an irrational and that is what I am trying to show. Also, would a similar proof work to show that an irrational + irrational = irrational?