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Proof root N is irrational

  1. Jun 13, 2011 #1
    I came across this question. How do you show that √N is irrational when N is a nonsquare integer?

  2. jcsd
  3. Jun 14, 2011 #2
    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


    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. Jun 16, 2011 #3
    Nice. Thanks hammster143. Appreciate it.

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