Square root vs raising to $\frac{1}{2}$ What about the +/- ??? These seem equivalent, yet the raising to 1/2 seems to ignore the +/- aspect of a square root.   Is one more valid than the other?


When you get a little further in math, you'll be told that raising a number to any exponent with a non-integer absolute value is what's called a "multi-valued function."  It's just that with a rational exponent with an even denominator it's two of these that are real rather than one as for any other real exponent.  Most of the time, the "principal value" is used, which for a positive real parameter is the positive real value.
