Cube root 42,875 using abacus (Triple-root method 2)

[Set 42,875 on Mr. Cube root]Zoom

[Japanese]

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 2-digits case and multiplication-back (wound up multiplying - Kakemodoshi in Japanese) by 9 occurs. 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 Square root of 42,875
(Answer is 35)

"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.

42,875 -> (042|875) : 42 is the 1st group number. The root digits is 2.

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Step 1: Set 42875. First group is 42.

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Step 2: Cube number smaller than 42 is 27=3^3. Place 3 on E as 1st root.

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Step 3: Place 42-27=15 on HI. (-a^3)

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Step 4: Place Triple root 3x3=9 on B.

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Step5: Repeat division by triple root 9 until 4th digits next to 1st root.(÷3a)

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Step 6: 15/9=1 remainder 6. Place 1 on G. Place 06 on HI.

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Step 7: Focus on 68.

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Step 8: Divide 68 by triple root 9.

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Step 9: 68/9=7 remainder 5. Place 7 on H and 05 on IJ.

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Step 10: Divide 57 by 9.

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Step 11: 57/9=6 remainder 3 Place 6 on I.

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Step 12: Place remainder 03 on JK.

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Step 13: Divide 17 by current root (1st root) 3. (÷a)

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Step 14: Ansewer is 5 and place 5 on F as 2nd root.

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Step 15: Place 17-1st root x Answer=17-3x5=02 on GH. (-ab)

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Step 16: Focus on 26 on HI.

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Step 17: Place 26-2nd root^2=26-5^2=01 on HI. (-b^2)

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Step 18: 1 on I is part of the remainder of the divisions by triple root from Step 5, multiply-back by triple root 9 as follows.

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Step 19: Place 0 on I.

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Step 20: Focus on 03 on JK.

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Step 21: Add 09 (multiply-back) to 03 on JK. Place 03+09=12 on JK.

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Step 22: Focus on 125 on JKL.

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Step 23: Focus on 2nd root 5.

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Step 24: 125-2nd root^3=125-5^3=0. Place 000 on JKL. (-b^3)

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Step 25: Cube root of 42875 is 35.

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Final state: Answer 35

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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


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