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Prove that 5^(2/3) is irrational

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that 5^(2/3) is irrational

    2. Relevant equations



    3. The attempt at a solution

    I tried writing a proof but that is not getting me any where.

    This is what I did so far -

    Show that 52/3 is irrational

    Proof: Suppose that 52/3 is rational:
    52/3 = a/b
    52/33/2 = a3/2/b3/2
    5(b3/2) = a3/2
    Substitute a = 2n + 1, b = 2m + 1;

    I don't know if I'm suppose to do like this?
     
  2. jcsd
  3. Oct 10, 2012 #2

    Mark44

    Staff: Mentor

    It might be simpler to use the fact that 52/3 = ##\sqrt[3]{25}##
     
  4. Oct 10, 2012 #3
    :approve:
    Gracias
     
  5. Oct 10, 2012 #4

    Mark44

    Staff: Mentor

    De nada
     
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