Problem calculating an expression with roots

02032015, 10:55 AM
(This post was last modified: 02032015 12:26 PM by retoa.)
Post: #27




RE: Problem calculating an expression with roots
(02022015 12:53 PM)parisse Wrote: ...because the expression is not defined for all values of x (or ambiguous like the definition of x^(1/3) for x<0). Parisse, I agree with you that working with nth roots is not very useful, I think I never found such expressions in real life calculation and it is very difficult to find practical examples with roots above the 3rd (except the 12th root of 2 in music, but you don't have a variable in it). But I still have a question about x^(1/3) for x<0. If I try to calculate (8)^(1/3), one solution is 2, because (2)^3=8 In CAS mode the Prime gives one of the complex solutions, 1+sqrt(3) i In home it gives the complex solution if you enable complex numbers and an error if you don't. 3rd root of (8) gives 2 (both in home and CAS) Why does the Prime give a complex solution to (8)^(1/3) and not the trivial one 2? And why does the Prime in home mode not give the 2 solution when it works with real numbers? As a comparison I tried to calculate (8)^(1/3) on other platforms: HP 11C : Error 0 HP 35s : INVALID y^x (or 1 i sqrt(3) if you use 8 i 0 ) Casio fx82 solar : 2 TI30X Pro : 2 TI nspire CAS : 2 WP 34S : Domain Error Elektronika MK56 : Error Calculator application in linux mint: 2 Maxima : 2 Wolfram aplha : 1+sqrt(3)i So it seems to be more a philosophical question, cause any producer choose his own way, but would it not be better to give the real solution 2 ? Kind regards Reto 

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