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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. 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 474,552
(Answer is 78)

"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.

474,552 -> (474|552): 474 is the 1st group number. The root digits is 2.


Step 1: Place 474552 on GHIJKL.


Step 2: The 1st group is 474.


Step 3: Cube number ≦ 474 is 343=7^3. Place 7 on C as the 1st root.


Step 4: Subtract 7^3 from the 1st group 474. Place 474-7^3=131 on GHI.


Step 5: Focus on 131552 on GHIJKL.


Step 6: Divide 131552 by 3. Place 131552/3=043850.6をGHIJKLM.


Step 7: Focus on 43 on HI.


Step 8: Repeat division by triple root 7 until 4th digits next to 1st root. 43/7=6 remainder 1. Place 6 on E.


Step 9: Place remainder 01 on HI.


Step 10: Divide 18 on IJ by current root 7. 18/7=2 remainder 4


Step 11: Place 2 on F.


Step 12: Place 04 on IJ.


Step 13: Divide 45 on JK by current root 7. 45/7=6 remainder 3


Step 14: Place 6 on G.


Step 15: Place 03 on JK.


Step 16: Divide 62 on EF by current root 7. 62/7=8 remainder 2


Step 17: Place 8 on D as 2nd root.


Step 18: Place 06 on EF.


Step 19: Subtract 2nd root^2 from 66 on FG. 66-8^2=2


Step 20: Place 02 on FG.


Step 21: 02 on FG x 1st root and add 03.0 on JKL. 2X7+3.0=17.0


Step 22: Place 17.0 on JKL.


Step 23: Subtract 2nd root^3/3 from 170.6 on JKLM. 170.6-8^3/3=0


Step 24: Place 000.0 on JKLM.


Step 25: Cube root of 474552 is 78.


Final state: Answer 78

Abacus state transition. (Click to Zoom)



Next article is also 1/3-multiplication table method, root is 2-digits case.


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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