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What rule am I breaking here?

  1. Mar 8, 2009 #1
    I have come up with a simple "paradox" (obviously I am doing something wrong). Sorry I can't use latex:

    (-1)/1=1/(-1), take square root of both sides, so sqrt((-1)/1)=sqrt(1/(-1))
    use sqrt(a/b)=srt(a)/sqrt(b) *, so i/1=1/i, implies i squared =1.

    I think the problem is the part marked *, but I'm not sure in what circumstances this is valid. Can anybody help?
  2. jcsd
  3. Mar 8, 2009 #2
    The problem is that every number except 0 actually has two square roots with opposite sign. You can arbitrarily choose one for each number, but then the formula sqrt(a/b)=srt(a)/sqrt(b) is not always true (as you demonstrated).

    See also http://en.wikipedia.org/wiki/Square_root#Notes"
    Last edited by a moderator: Apr 24, 2017
  4. Mar 8, 2009 #3
    Ok that helps a lot. The example on wikipedia was pretty much exactly the one I posted. Thanks.
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