Paper-and-pencil nth 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×(02)×1+30×0×(12)+13 - 2 000 1 744 = 300×(12)×4+30×1×(42)+43 ----- 256 000 241 984 = 300×(142)×4+30×14×(42)+43 ------- 14 016 000 12 458 888 = 300×(1442)×2+30×144×(22)+23 ---------- 1 557 112 000 1 247 791 448 = 300×(14422)×2+30×1442×(22)+23 ------------- 309 320 552 000 249 599 823 424 = 300×(144222)×4+30×14422×(42)+43 --------------- 59 720 728 576Note that after the first iteration or two the leading term dominates the, so we can get an often correct first guess at β by dividing by .
Read more about this topic: Shifting nth Root Algorithm
Famous quotes containing the word roots:
“Though of erect nature, man is far above the plants. For man’s superior part, his head, is turned toward the superior part of the world, and his inferior part is turned toward the inferior world; and therefore he is perfectly disposed as to the general situation of his body. Plants have the superior part turned towards the lower world, since their roots correspond to the mouth, and their inferior parts towards the upper world.”
—Thomas Aquinas (c. 1225–1274)