Is This the Easiest Proof That n th Roots are Always Integers or Irrational?
Jeffrey Bergen · Mathematics Magazine · 2017
SummaryMost proofs that nth roots of positive integers are always integers or irrational involve concepts such as prime numbers, relative primeness, or the fundamental theorem of arithmetic. We provide an argument which uses only the well ordering principle and the division algorithm. You can decide if it is the easiest proof possible.