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Homework Help: Simple field question

  1. Feb 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose F=Q(a_1,a_2,...,a_n) where a_i^2 is in Q for i=1,2,...,n. Prove that 2^(1/3)
    is not in F.


    3. The attempt at a solution

    Someone suggested the tower law.. I have no idea what that is. Isn't this true because if 2^(1/3) was in F then 2^(2/3) must be in Q, but 2^(2/3) is irrational so it cannot be so 2^(2/3) is not in F. Is this right?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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