Difference between revisions 846010456 and 849849718 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)===Square root of 3===
      1. 7  3  2  0  5
     ----------------------
 _  / 3.00 00 00 00 00
  \/  1 = 20×0×1+1^2
      -
      2 00
      1 89 = 20×1×7+7^2
 (27 x 7)
      ----
        11 00
        10 29 = 20×17×3+3^2  (343 x 3)
        -----
           71 00
           69 24 = 20×173×2+2^2 (3462 x 2)
           -----
            1 76 00
                  0 = 20×1732×0+0^2 (34640 x 0)
            -------
            1 76 00 00
            1 73 20 25 = 20×17320×5+5^2 (346405 x 5)
            ----------
               2 79 75

===Cube root of 5===
      1.  7   0   9   9   7
     ----------------------
 _ 3/ 5. 000 000 000 000 000
(contracted; show full)* [[Methods of computing square roots]]

==External links==
*[http://www.homeschoolmath.net/teaching/sqr-algorithm-why-works.php Why the square root algorithm works] "Home School Math". Also related pages giving examples of the long-division-like pencil and paper method for square roots.

[[Category:Root-finding algorithms]]
[[Category:Computer arithmetic algorithms]]
[[Category:Digit-by-digit algorithms]]