radical problem

[daon2]

Yes, but you made it a matter of choice, and so the "usual" translation from exponents to radicals no longer holds.

It is also true that \(\displaystyle (-1)^{2/3} = -1/2-\sqrt{3}/2i\) and that \(\displaystyle (-1/2-\sqrt{3}/2i)^{3/2} = -1\)

 

[cschulz57919]

Re: JeffM

I thought you had done the math for the other one and saw it wasnt applicable, because the domain changed. the answer you gave was the correct one, and from you explaination, I was able to explain why one worked and one didnt.
Thanks to your help, my homework grades were 20/20, 20/20, 19/20,18/20.
Dont beat yourself up, you followed my logic and had it make logical sense to me

Thanks all.

cschulz57919

 

[cschulz57919]

The principal complex root is real if x is non-negative, so 20.032 is the answer. 19.968 is only correct if one defines

when

which can cause "paradoxes"
X^a/b must equal both (b root of x)^a and (b rootof x^a)

 

[pka]

This has been one of the most frustrating threads.I thought that I knew why some could disagree on how these were calculated. But then then I was reviewing some lessons for a computer algebra system built on MathCad, a widely used CAS in engineering schools. Playing around I typed in this very problem expecting to get one real solution. To my surprise it gave me two, see the attachment.

 

[daon2]

I think there is disagreement of CAS's on what exactly a rational power means. My TI-89 emulator also gives two solutions, but a program like mathematica will give 1. Some will graph x^(2/3) as being positive for x<0, others it will be undefined. I'm over it though.