Difference between revisions 259757979 and 259789211 on enwiki

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)                1 01 11 remainder

===Square root of 3===

      1. 7  3  2  0  5
     ----------------------
    / 3.00 00 00 00 00
 /\/  1 = 20
*0*×0×1+1^2
      -
      2 00
      1 89 = 20*1*×1×7+7^2
      ----
        11 00
        10 29 = 20*×17*×3+3^2
        -----
           71 00
           69 24 = 20*×173*×2+2^2
           -----
            1 76 00
                  0 = 20*×1732*×0+0^2
            -------
            1 76 00 00
            1 73 20 25 = 20*×17320*×5+5^2
            ----------
               2 79 75

===[[Cube root]] of 5===

      1.  7   0   9   9   7
     ----------------------
(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]]