Question #987b8
1 Answer
If the index is even, you get a nonreal complex number.
Explanation:
This is what I call the "even/odd problem."
Simple example using "2" (but any number works).
We see that
Therefore,
Since this is true for any nonzero real number, x, we see that
However, notice that when we multiply an even number of negative factors, the product is POSITIVE.
If there are an even number of factors, the product is always positive. Therefore, all real even roots are roots of positive numbers.
What happens with something like
As we saw a moment ago, there is no real number whose square is negative. Therefore
At the lower levels we simply say it is undefined.
Later on, we observe that