Cube root [HP-35]

[Albert Chan]

(03-20-2020 02:10 PM)Gerson W. Barbosa Wrote:  (Taken from http://ajmonline.org/2008/5.pdf)

Thanks for the link.

Setup as interation formula, this also have cubic convergence, slightly better than Pade[1,1]

\(\large \sqrt[3]k ≈\left(x + \sqrt{4k\;-\; x^3 \over 3x}\right) ÷ 2\)

Note: guess x can be at most 4^(1/3)-1 ≈ 58% above true value of \(\sqrt[3]k\)

Code:

STO 0    ; HP-12C code for cube root
Enter
Enter
×
×
CHS
X<>Y
4
×
+
RCL 0
3
×
/
SQRT
RCL 0
+
2
/

4.1 Enter 2
R/S     → 1.591607979
R/S     → 1.600520756
R/S     → 1.600520664

100 Enter 5
R/S     → 4.640872096
R/S     → 4.641588834