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Today's example is also about actual solution of Cube root using abacus. The calculation becomes more complicated than previous example.

Today's example is simple - basic Triple-root method, root is 3-digits and there is zero in the middle of root. Please check the Theory page for your reference.

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 128,024,064
(Answer is 504)

"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.

128,024,064 -> (128|024|064): 128 is the 1st group number. The root digits is 3.


Step 1: Set 128024064. First group is 128.


Step 2: Cube number smaller than 128 is 125=5^3. Place 5 on D as 1st root.


Step 3: Place 128-125=003 on GHI. (-a^3)


Step 4: Place Triple root 3x5=15 on AB.


Step 5: Repeat division by triple root 15 until 4th digits next to 1st root. 30/15=2 remainder 0. Place 2 on G. (÷3a)


Step 6: Place remainder 00 on IJ.


Step 7: Cannot get answer of division on H. Continue division by triple root. 240/150=1 remainder 90.


Step 8: Place 1 on I.


Step 9: Place remainder 090 on KLM.


Step 10: 906/150=6 remainder 6


Step 11: Place 6 on J.


Step 12: Place remainder 006 on LMN.


Step 13: Divide 201 by current root 50 on DE.


Step 14: Place 4 on F as 3rd root.


Step 15: Place remainder 001 on GHI.


Step 16: Subtract 3rd root^2 from 16 on IJ.


Step 17: Place 16-4^2=00 on IJ. (-c^2)


Step 18: Subtract 3rd root^3 from 64 on NO.


Step 19: Place 64-4^3=00 on NO. (-c^3)


Step 20: Cube root of 128024064 is 504.


Final state: Answer 504

Abacus state transition. (Click to Zoom)



Next article is also about Cube root calculation (Triple-root method).


Related articles:

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

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


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