Difference between revisions 272257949 and 272257979 on enwiki

{{Cleanup|date=December 2008}}

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 a manner similar to [[long division]].

==Algorithm==
(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
      -
      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]]