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Shifting nth root algorithm
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==

===Notation===

(contracted; show full)             52 164 383 027

===Fourth root of 7===

      1.   6    2    6    5    7
     ---------------------------
 _ 4/ 7.0000 0000 0000 0000 0000
  \/  1 = 4000
*×(0^3)*×1+400*×(0^2)*×(1^2)+40*0*×0×(1^3)+1^4
      -
      6 0000
      5 5536 = 4000*×(1^3)*×6+600*×(1^2)*×(6^2)+40*1*×1×(6^3)+6^4
      ------
        4464 0000
        3338 7536 = 4000*×(16^3)*×2+600*(16^2)*×(2^2)+40*×16*×(2^3)+2^4
        ---------
        1125 2464 0000
        1026 0494 3376 = 4000*×(162^3)*×6+600*×(162^2)*×(6^2)+40*×162*×(6^3)+6^4
        --------------
          99 1969 6624 0000
          86 0185 1379 0625 = 4000*×(1626^3)*×5+600*×(1626^2)*×(5^2)+
          -----------------   40*×1626*×(5^3)+5^4
          13 1784 5244 9375 0000
          12 0489 2414 6927 3201 = 4000*×(16265^3)*×7+600*×(16265^2)*×(7^2)+
          ----------------------   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]]