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    \$\begingroup\$ This deserves a +1. I've been refactoring generalized nth root algs for the last hour, and I just now arrived at the same result. Bravo. \$\endgroup\$ Commented Feb 22, 2014 at 14:47
  • \$\begingroup\$ @primo I instantly recalled all n'th root approximation algorithms, and after giving up on Taylor/Maclaurin series in APL I used this. \$\endgroup\$ Commented Feb 22, 2014 at 15:28
  • \$\begingroup\$ Using Newton method I got x=(2*x+n/x/x)/3, can you explain why you can use x=(x+n/x/x)/2 ? It converges slower but I can't explain why it converges... \$\endgroup\$ Commented Feb 22, 2014 at 15:42
  • \$\begingroup\$ @Michael because if you take x=cbrt(n), then x=(x+n/x/x)/2 is true. So is it true for your expression \$\endgroup\$ Commented Feb 22, 2014 at 15:50
  • \$\begingroup\$ @Michael I got there this way: codepad.org/gwMWniZB \$\endgroup\$ Commented Feb 22, 2014 at 16:03