Hey mathematicians, why is (odd integer) root of a negative number undefined behaviour?

  _____
³?-27 = -3 ?
-3 · -3 = 9
9 · -3 = -27
 

Why do you say it's undefined? My desktop calculator works fine with odd roots of negative numbers.

EDIT: FYI, you posted in the Math & Physics forum. Do you perhaps have a programming question, instead?

What is the context of the undefined behavior? Particular program or language? Calculator?

If you're using a software to compute it and it answers undefined, maybe it has a bug. Check this post: http://math.stackexchange.com/questions/25528/cubic-root-of-negative-numbers

Even Wolfram Alpha had a bug because of other possible answers (complex numbers), but it looks like now it shows you the real one and there's an option to check the complex ones too.

Hey mathematicians, why is (odd integer) root of a negative number undefined behaviour?

  _____
³?-27 = -3 ?
-3 · -3 = 9
9 · -3 = -27
 

Is this becoming a hobby of yours? You ask why something is not the way it should be, but it actually IS the way it should be. You can initialize multi-dimensional arrays in C or C++ to zero by specifying only the first element, and the odd-integer root of a negative number is perfectly well defined.

Good old Windows calculator:

It is a problem of the Windows Vista Calculator then. In Windows 7 it works perfectly.

Just out of curiosity, try: (-27)^(1/3) in the calculator to see if you get an answer.

The INV button is not meant to be used with the power buttons in calc.exe - It's more obvious on the Windows 8 desktop version because it re-labels the buttons which it applies to.

Do what Javier says and use a fractional power: -27 x^y (1/3) (or the new "y root x" button if you have a new enough version)

Good old Windows calculator:

Here's some advice on how to ask questions on these forums:
* Try to find the answer for yourself first. For instance, using Google. You do have an Internet connection, don't you?
* If you still can't find the answer, post enough detail that we know what the situation is, why you think it's wrong, etc.


Let me illustrate what "enough detail" means:
I tried to compute the cubic root of -27 in Windows Calculator [version blah] and I get an error message that would translate to "invalid value". Shouldn't the answer be -3? Is this a bug?

It is a problem of the Windows Vista Calculator then. In Windows 7 it works perfectly.

Just out of curiosity, try: (-27)^(1/3) in the calculator to see if you get an answer.

I get the same "invalid value" message. I used 0,333333333333333333333333333333 instead of 1/3 (since otherwise it would raise it to the first and then divide by three)

(or the new "y root x" button if you have a new enough version)

If you check the gif I linked to, there is no "y root of x" option.