The xth root of y on the hp 35s



#5

While quickly going through the first few chapters of the manual to get acquainted with the 35s, I came across an example on page 4-3 which shows the calculation of 3th root of -125 to be -5.

This perked my interest since I was under the impression that taking any xth root of a negative number is not possible on the 35s.

I performed the example, then tried calculating the xth of a handful of negative numbers.

Conclusion?

It only works if x is odd (and y can be any negative real numbers). If x is even, it will fail.

The only condition mentioned on the page is that for y<0, x must be an integer.

Can someone tell me why?

My guess is that the condition should be for y<0, x must be an even integer.

Thanks.


#6

Quan --

"x-th root of y" on the HP-35s (and its predecessors HP-33s and HP-32SII) has a real-valued range and real-valued domain of x and y. The negative real-valued odd root of a negative number can be obtained. However, complex-valued roots cannot be obtained with the function, and complex-valued inputs are invalid.

The domain and range of "y^x" do encompass complex numbers, but there are some peculiarities. Please see the following archived posts:

"x_root_y" and real vs. complex roots

35s complex-number functionality

-- KS

Edited: 30 May 2009, 11:12 p.m.

#7

Hi Quan

Since real valued roots are (apparently) all the 35S will return, and since a negative real number has 1 real odd root, that's what is returned. Since that same negative real has no real valued even roots (they're all complex), nothing is returned. All the even or odd roots of any number, real or complex, are relatively easy to come up with (DeMoivre's Theorum), but it would be nice if the calculator would just give them to you. If the 35s will solve for the zero's of a polynomial (I don't have a 35s, so I don't know), a workaround would be to transform to polynomial form and get the roots that way (cube root -8 would be (x^3 + 8), and the three cube roots (ie zero's) returned would be (in polar form) 2@60deg, 2@180deg (ie,-2), and 2@-60deg.


Best regards, Hal


#8

Karl, Hal:

Thanks for the informative responses.

I sometimes forgot and expected more from HP calculators to give me the answers.

Regards,

Quan


Possibly Related Threads...
Thread Author Replies Views Last Post
  [HP Prime] Using n-root symbol and exponent problem uklo 7 918 11-11-2013, 01:39 AM
Last Post: Alberto Candel
  Cubic root (-8) = 2 ? Gilles Carpentier 37 3,003 08-12-2013, 10:26 PM
Last Post: jep2276
  Square Root Simplifier for HP39gII Mic 4 637 03-11-2013, 08:25 AM
Last Post: Eddie W. Shore
  Cube root on standard calculator Thomas Klemm 22 2,045 11-09-2012, 06:11 AM
Last Post: Pierre
  ROOT bug? HP 48S/48G Eddie W. Shore 8 845 07-13-2012, 07:05 PM
Last Post: Eddie W. Shore
  x root y on hp42s David Griffith 14 1,183 04-08-2012, 12:43 PM
Last Post: Walter B
  35s prompt for multi-character variables in program like "low footprint" root finder Chris C 8 914 02-14-2012, 06:52 PM
Last Post: Chris C
  [WP34S] SLV returns "Failed" when it finds a root just fine. Les Wright 6 669 11-27-2011, 04:31 PM
Last Post: Paul Dale
  WP34S: Valentin Albillo's Polynomial Root Finder Miguel Toro 28 2,218 11-23-2011, 07:39 PM
Last Post: Miguel Toro
  Results of new root-seeking methods Namir 3 415 08-22-2011, 03:28 PM
Last Post: C.Ret

Forum Jump: