![](https://blogimg.goo.ne.jp/user_image/5b/45/5f84e0f320c9c203696e4a887729b294.png)
[Set 474,552 on Mr. Cube root]
[Japanese]
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.
![](https://blogimg.goo.ne.jp/user_image/31/6d/8f70c7a3cdcfc4f14d585e0e206ae763.png)
Step 1: Place 474552 on GHIJKL.
![](https://blogimg.goo.ne.jp/user_image/4a/3f/66eadc7515ba7c3c7b8a6b40ca0d2281.png)
Step 2: The 1st group is 474.
![](https://blogimg.goo.ne.jp/user_image/47/7d/d7e8878b5143f25a0498afb2b62957ea.png)
Step 3: Cube number ≦ 474 is 343=7^3. Place 7 on C as the 1st root.
![](https://blogimg.goo.ne.jp/user_image/4b/1f/4a3ebaf1c2d4306de85867e69c0151f1.png)
Step 4: Subtract 7^3 from the 1st group 474. Place 474-7^3=131 on GHI.
![](https://blogimg.goo.ne.jp/user_image/31/bc/7969b7667dce26f4e1776e8b17432f5d.png)
Step 5: Focus on 131552 on GHIJKL.
![](https://blogimg.goo.ne.jp/user_image/1f/80/a1e05eb33e40057cc540f2e4d0a6f187.png)
Step 6: Divide 131552 by 3. Place 131552/3=043850.6をGHIJKLM.
![](https://blogimg.goo.ne.jp/user_image/2b/9e/437122560defa57ebda98396c5b20dd9.png)
Step 7: Focus on 43 on HI.
![](https://blogimg.goo.ne.jp/user_image/02/e4/cb5bc62649276206316c21d611a746de.png)
Step 8: Repeat division by triple root 7 until 4th digits next to 1st root. 43/7=6 remainder 1. Place 6 on E.
![](https://blogimg.goo.ne.jp/user_image/29/31/a72052bf3aa1867fe994bee8182aa8cc.png)
Step 9: Place remainder 01 on HI.
![](https://blogimg.goo.ne.jp/user_image/16/36/3cf47e5cc156ec319e179415d7dc54d9.png)
Step 10: Divide 18 on IJ by current root 7. 18/7=2 remainder 4
![](https://blogimg.goo.ne.jp/user_image/2d/a7/e459dfdfffb275b858cc39634ff3f279.png)
Step 11: Place 2 on F.
![](https://blogimg.goo.ne.jp/user_image/5a/46/c450c61b99a6ab6fa8658bcddde754b0.png)
Step 12: Place 04 on IJ.
![](https://blogimg.goo.ne.jp/user_image/6a/a5/71730e779bb2229367ccce97747691c8.png)
Step 13: Divide 45 on JK by current root 7. 45/7=6 remainder 3
![](https://blogimg.goo.ne.jp/user_image/56/a3/36b61a547412a9da16a2be8f836f8908.png)
Step 14: Place 6 on G.
![](https://blogimg.goo.ne.jp/user_image/48/91/ae07a50c7a2883eb58e06d78f6d9d49b.png)
Step 15: Place 03 on JK.
![](https://blogimg.goo.ne.jp/user_image/30/8b/58f438bebc0b0977e3e9442303e541d9.png)
Step 16: Divide 62 on EF by current root 7. 62/7=8 remainder 2
![](https://blogimg.goo.ne.jp/user_image/08/3b/f0bad1f60b907509024be7f26d38d41f.png)
Step 17: Place 8 on D as 2nd root.
![](https://blogimg.goo.ne.jp/user_image/17/d1/36d4bc3d62f7e5d51e0067047e58d570.png)
Step 18: Place 06 on EF.
![](https://blogimg.goo.ne.jp/user_image/24/31/5d9d5f37b01dc11d24170f85af78200e.png)
Step 19: Subtract 2nd root^2 from 66 on FG. 66-8^2=2
![](https://blogimg.goo.ne.jp/user_image/07/33/eab392ae483131538e65947475effad4.png)
Step 20: Place 02 on FG.
![](https://blogimg.goo.ne.jp/user_image/2e/7d/888befba222697d2500f2d7ffe125ae5.png)
Step 21: 02 on FG x 1st root and add 03.0 on JKL. 2X7+3.0=17.0
![](https://blogimg.goo.ne.jp/user_image/7d/30/e9de816ef55c58e3beb21c8bf45220aa.png)
Step 22: Place 17.0 on JKL.
![](https://blogimg.goo.ne.jp/user_image/14/48/b70a583c5f5fe110372e7a67d1199cda.png)
Step 23: Subtract 2nd root^3/3 from 170.6 on JKLM. 170.6-8^3/3=0
![](https://blogimg.goo.ne.jp/user_image/35/7f/81dfc22da22103eb2967aa8793425ffd.png)
Step 24: Place 000.0 on JKLM.
![](https://blogimg.goo.ne.jp/user_image/00/33/6e92274285d9532e53cb741c9a19d2cf.png)
Step 25: Cube root of 474552 is 78.
![](https://blogimg.goo.ne.jp/user_image/22/33/b87fb5f65bb1b62377ce45a39967b7b7.png)
Final state: Answer 78
Abacus state transition. (Click to Zoom)
![](https://blogimg.goo.ne.jp/user_image/15/8f/8bb43506d70b587ca879434b77037dca.png)
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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