Proof root N is irrational

  1. I came across this question. How do you show that √N is irrational when N is a nonsquare integer?

    Cheers.
     
  2. jcsd
  3. It depends on what you're allowed to use.

    But the simplest way would be to use the fundamental theorem of arithmetic (that every integer has a unique prime factorization). For any N, if sqrt(N) is rational, you can write that as

    N=A^2/B^2

    and therefore

    B^2 N = A^2

    and it's not hard to get from that + the fundamental theorem to the conclusion that N is a square.
     
  4. Nice. Thanks hammster143. Appreciate it.

    bgwyh_88
     
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