Why is the odd integer rootof a negative number undefined?

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

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


Edited by gasto

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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?

Edited by Buckeye

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

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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.

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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.

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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.

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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) Edited by Nypyren

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Good old Windows calculator:

* 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?

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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.

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