Question 50
You are given some positive integer $n$. Prove that for any real numbers $a_1, a_2, ..., a_n$ there exists some number of form $k\sqrt{2}$, where $k$ is some positive integer, that all numbers $k\sqrt{2} + a_1, k\sqrt{2} + a_2, ..., k\sqrt{2} + a_n$ are irrational.