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What IS a radical?

  1. Nov 1, 2012 #1
    I'm currently writing a proof that relates to continuity of a bizarre function and I ran across an interesting thought, at least to me. I don't really know what a radical √ is. For example, 6^3 is:

    6*6*6

    and x^n is:

    x*x*x*x*x*x*x*x*x*x, n times, but what is a square root (ie. radical)? It's the opposite of a power, but I don't know how to define it!

    Thanks!
     
  2. jcsd
  3. Nov 1, 2012 #2

    arildno

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    A number "a" is the square root
    of a number "b", if a*a=b.
    that's the definition you may work with at present, and it is sufficient for most purposes.
     
  4. Nov 1, 2012 #3
    I guess I should be slightly more specific about the work I am doing. What about the radical of a function? Could it be defined as f(x)=g(x)*g(x)?

    [itex]\sqrt{f(x)}[/itex]
     
  5. Nov 1, 2012 #4

    micromass

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    You should demand a to be positive as well.
     
  6. Nov 1, 2012 #5

    arildno

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    "the" is "the (positive)" in Norwegian.
    It is not my fault that you are as incompetent in Norwegian as I am in Zulu. :smile:
     
  7. Nov 2, 2012 #6

    HallsofIvy

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    No, but if you expecting Norwegian usages to carry over to Engish, it is.
     
  8. Nov 2, 2012 #7

    Erland

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    Well, ##\sqrt{a}=a^{1/2}## if ##a>0##.
     
  9. Nov 2, 2012 #8

    arildno

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    Only if I am polite. :smile:
     
  10. Nov 2, 2012 #9

    Bacle2

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    Maybe you're looking for something like this:

    http://en.wikipedia.org/wiki/Functional_calculus ?
     
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