Difference between revisions 1002655775 and 1101418271 on enwiki

{{DISPLAYTITLE:Shifting ''n''th root algorithm}}
{{unreferenced|date=May 2010}}
The '''shifting ''n''th root algorithm''' is an [[algorithm]] for extracting the [[nth root|''n''th root]] of a positive [[real number]] which proceeds iteratively by shifting in ''n'' [[numerical digit|digits]] of the radicand, starting with the most significant, and produces one digit of the root on each iteration, in (contracted; show full) _ 3/ 5. 000 000 000 000 000
  \/  1 = 300×(0^2)×1+30×0×(1^2)+1^3
      -
      4 000
      3 913 = 300×(1^2)×7+30×1×(7^2)+7^3
      -----
         87 000
              0 = 300×(17^2
)×0+30×17×(0^2)+0^3
        -------
         87 000 000
         78 443 829 = 300×(170^2)×9+30×170×(9^2)+9^3
         ----------
          8 556 171 000
          7 889 992 299 = 300×(1709^2)×9+30×1709×(9^2)+9^3
          -------------
(contracted; show full)
*[https://q12.medium.com/reflections-on-the-square-root-of-two-ae792db4c7e Reflections on The Square Root of Two] "Medium". With an example of a C++ implementation.
[[Category:Operations on numbers]]
[[Category:Root-finding algorithms]]
[[Category:Computer arithmetic algorithms]]
[[Category:Digit-by-digit algorithms]]