Difference between revisions 383993243 and 383993346 on enwiki

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Shifting nth root algorithm
{{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)

==Paper-and-pencil ''n''th roots==
As noted above, this algorithm is similar to long division, and it lends itself to the same notation:

      1.  4   4   2   2   4
     ----------------------
 _ 3/ 3.000 000 000 000 000
  \/  1 = 300×(0
^2)×1+30×0×(1^2)+1^3<sup>2</sup>)×1+30×0×(1<sup>2</sup>)+1<sup>3</sup>
      -
      2 000
      1 744 = 300×(1<sup>2</sup>)×4+30×1×(4<sup>2</sup>)+4<sup>3</sup>
      -----
        256 000
        241 984 = 300×(14<sup>2</sup>)×4+30×14×(4<sup>2</sup>)+4<sup>3</sup>
        -------
(contracted; show full)          ----------------------   40×16265×(7^3)+7^4
           1 1295 2830 2447 6799

[[Category:Root-finding algorithms]]

[[de:Schriftliches Wurzelziehen]]
[[fr:Algorithme de décalage n-racines]]
[[nl:Worteltrekken]]