Cube root 59,319 using abacus (1/3-multiplication table method 4)

[Set 59,319 on Mr. Cube root]

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Following the last time, today's example is about actual solution of Cube root using abacus.

Today's example is simple - basic 1/3-multiplication table method, root is 2-digits case and and we require 9 as root in the steps. You can check the Index page of all articles.

Cube root methods: Triple-root method, constant number method, 3a^2 method, 1/3-division method, 1/3-multiplication table method, 1/3-multiplication table alternative method, Multiplication-Subtraction method, 3-root^2 method, Mixing method, Exceed number method, Omission Method, etc.


Abacus steps to solve Cube root of 59,3192
(Answer is 39)

"1st group number" is the left most numbers in the 3-digits groups of the given number for cube root calculation. Number of groups is the number of digits of the Cube root.

59,319 -> (59|319): 59 is the 1st group number. The root digits is 2.


Step 1: Place 59319 on HIJKL.


Step 2: The 1st group is 59.


Step 3: Cube number ≦ 59 is 27=3^3. Place 3 on C as the 1st root.


Step 4: Subtract 3^3 from the 1st group 59. Place 59-3^3=32 on HI.


Step 5: Focus on 32319 on HIJKL.


Step 6: Divide 32319 by 3. Place 32319/3=10773 on HIJKL.


Step 7: Focus on 10 on HI.


Step 8: Repeat division by triple root 4 until 4th digits next to 1st root. 10/3=3 remainder 1. Place 3 on E.


Step 9: Place remainder 01 on HI.


Step 10: Divide 17 on IJ by current root 3. 17/3=5 remainder 2


Step 11: Place 5 on F.


Step 12: Place 02 on IJ.


Step 13: Divide 27 on JK by current root 3. 27/3=9 remainder 0


Step 14: Place 9 on G.


Step 15: Place 00 on JK.


Step 16: As the last digit of EFG equals to the last digit of current root C x3, we set 9 on D as 2nd root.


Step 17: Divide 35 on EF by current root 9. 35/9=3 remainder 8.


Step 18: Place 02 on EF.


Step 19: Place 89-2nd root^2=89-9^2=08 on FG.


Step 20: 08 on FG x 1st root 3 + 00 on JK. Place 3x8+0=24 on JK.


Step 21: Subtract 2nd root 9^3/3 from 243 on JKL. 243-9^3/3=0


Step 22: Place 000 on JKL.


Step 23: Cube root of 59319 is 39.


Final state: Answer 39

Abacus state transition. (Click to Zoom)


It is interesting to compare with the Triple-root method.


Next article is also 1/3-multiplication table method.


Related articles:

How to solve Cube root of 1729.03 using abacus? (Feynman v.s. Abacus man)
https://blog.goo.ne.jp/ktonegaw/e/cff5d6e7ecaa07230b9cc7af10b23aed

Index: Square root and Cube root using Abacus
https://blog.goo.ne.jp/ktonegaw/e/f62fb31b6a3a0417ec5d33591249451b

Cube root 59,319 using abacus (Triple-root method 4)
https://blog.goo.ne.jp/ktonegaw/e/e5d49843b3bb4aa289d1f4faebd879d3


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