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I'm supposed to evaluate the following equation in the real number system f possible : (-9)^1/2.
The answer says it's not possible; why, I don't understand this.

  • Math -

    The problem is really how to define fractional powers like x^(1/2).

    You want it to define in such a way so that the usual rules for taking powers still hold. E.g.:

    (x^a)^b = x^(ab)

    This means that you want to define
    x^(1/2) such that:

    (x^(1/2))^2 = x

    So, x^(1/2) should be the square root of x. But this is only defined for positive x. The square of a real number is always positive, so if x is negative, no real number can be its square root.

  • Math -

    oh, okay, I see; thank you very much! :D

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