Posted by Luci on Thursday, October 23, 2008 at 10:49pm.
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  Count Iblis, Thursday, October 23, 2008 at 11:08pm
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.
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