Cube root 12,812,904 using abacus (1/3-multiplication table method 5)

[Set 12,812,904 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 3-digits case. 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 12,812,904
(Answer is 234)

"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.

12,812,904 -> (12|812|904): 12 is the 1st group number. The root digits is 3.


Step 1: Place 12812904 on HIJKLMNO.


Step 2: The 1st group is 12.


Step 3: Cube number ≦ 12 is 8=2^3. Place 2 on C as the 1st root.


Step 4: Subtract 2^3 from the 1st group 12. Place 12-2^3=04 on HI.


Step 5: Focus on 4812904 on IJKLMNO.


Step 6: Divide 4812904 by 3. Place 4812904/3=16043013 on IJKLMNOP.


Step 7: Focus on 16 on HI.


Step 8: Repeat division by current root 2 until 4th digits next to 1st root. 16/2=8 remainder 0. Place 8 on F.


Step 9: Place remainder 00 on IJ.


Step 10: Divide 8 on F by current root 2. 8/2=3 remainder 2


Step 11: Place 3 on D as 2nd root.


Step 12: Place 2 on F.


Step 13: Subtract 2nd root^2 from 20 on EF. 20-3^2=11


Step 14: Place 11 on FG.


Step 15: Add 1st root x remainder 11 to 00 on JK. 11X2+0=22


Step 16: Place 00 on JK.


Step 17: Subtract 2nd root/3 from 224 on JKL. 224-3^3=215


Step 18: Place 215 on JKL.


Step 19: Clear 11 on FG. Place 00 on FG.


Step 20: Divide by current root 23 from NOP.


Step 21: 215/23=9 remainder 8. Place 9 on G.


Step 22: Place 008 on JKL.


Step 23: 83/23=3 remainder 14. Place 3 on H.


Step 24: Place 14 on LM.


Step 25: 140/23=6 remainder 2. Place 6 on I.


Step 26: Place 002 on LMN.


Step 27: Divide 93 on GH by crrent root 23. 93/23=4 remainder 1


Step 28: Place 4 on E as 3rd root.


Step 29: Place 01 on GH.


Step 30: Subtract 3rd root^2 from 16 on HI. 16-4^2=0


Step 31: Place 00 on HI.


Step 32: Subract 3rd root/3 from 21.3 on NOP. 21.3-4^3/3=0


Step 33: Place 000 on NOP.


Step 34: Cube root of 12812904 is 234.


Final state: Answer 234

Abacus state transition. (Click to Zoom)




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


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