[?] Get cube roots with W|A?

Questions
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1

Critical Error in Math functions of roots! Square, four and other even roots have nice number line but odd roots are caltulated wrong here!
Some example here:
((x+2)(x^2+4x +1))^(1/3) are calculated wrong and have the same number line as ((x+2)(x^2+4x +1))^(1/2)!!

Maybe I have made a mistake but it seems unacceptable…

How should I use this site to avoid it or is it just a bug?

2

I assume this pertains to Wolfram|Alpha.

Try replacing the 1/3 power with CubeRoot[ ((x+2)(x^2+4x +1))].

It’s not a bug but rather a judgement call as to whether that power should be interpreted as the real-valued CubeRoot function, or the complex-valued principal third root (as written).

By the way, the plot is not identical to that of the square root, though they are similar.

3

Thanks a lot!