Recently in Algebra 2 we came upon a wierd problem.
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If you solve for x you get 1 but if you plug the answer, 1, back in the problem it does not come out correct.

However, the 6th root of 1 can come out to 1 or -1. If you use -1 then the problem does work, but if you use 1 it does not. (Calculators automatically use 1 because its the simpler answer.)

We have been arguing about this for days and our math teacher is going nuts, please send a reply for his sake ;-p

I like your question a lot. You ask an interesting question and then you essentually answer it yourselves.

The answer is that it depends what you mean by . If cannot be negative, as is the way your calculator works, then there is no number x so that . If, for positive x, is two values, one positive and one negative, then one of the values of is 3, the other value of is 5.

In order to remove this ambiguity mathematicians usually follow the convention that cannot be negative.

Penny and Maxine