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Prove if a belongs R, then (a^2)^1/2= |a|?

  1. Jul 27, 2010 #1
    Would you please help me? Thanks in advance.

    Prove that if a belongs to R, then (a^2)^1/2 = |a|?
    by using Abstract, Discrete, Algebraic Math.

    I work, but stuck:
    |a| =< (a^2)^1/2, then
    - (a^2)=< a =< (a^2)

    Please help!
     
    Last edited: Jul 27, 2010
  2. jcsd
  3. Jul 27, 2010 #2

    mathman

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    Depends on your definition of square root. The usual definition means you will have two answers a and -a. However if you insist that the square root be positive, the |a| is the positive root.
     
  4. Jul 27, 2010 #3
    If a >= 0, it's pretty much obvious; otherwise, consider -a.
     
  5. Aug 1, 2010 #4

    Hurkyl

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    Thread closed for user not showing any work.
     
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