[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
Abacus state transition. (Click to Zoom)
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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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[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.
Step 1: Set 42875. First group is 42.
Step 2: Cube number smaller than 42 is 27=3^3. Place 3 on E as 1st root.
Step 3: Place 42-27=15 on HI. (-a^3)
Step 4: Place Triple root 3x3=9 on B.
Step5: Repeat division by triple root 9 until 4th digits next to 1st root.(÷3a)
Step 6: 15/9=1 remainder 6. Place 1 on G. Place 06 on HI.
Step 7: Focus on 68.
Step 8: Divide 68 by triple root 9.
Step 9: 68/9=7 remainder 5. Place 7 on H and 05 on IJ.
Step 10: Divide 57 by 9.
Step 11: 57/9=6 remainder 3 Place 6 on I.
Step 12: Place remainder 03 on JK.
Step 13: Divide 17 by current root (1st root) 3. (÷a)
Step 14: Ansewer is 5 and place 5 on F as 2nd root.
Step 15: Place 17-1st root x Answer=17-3x5=02 on GH. (-ab)
Step 16: Focus on 26 on HI.
Step 17: Place 26-2nd root^2=26-5^2=01 on HI. (-b^2)
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.
Step 19: Place 0 on I.
Step 20: Focus on 03 on JK.
Step 21: Add 09 (multiply-back) to 03 on JK. Place 03+09=12 on JK.
Step 22: Focus on 125 on JKL.
Step 23: Focus on 2nd root 5.
Step 24: 125-2nd root^3=125-5^3=0. Place 000 on JKL. (-b^3)
Step 25: Cube root of 42875 is 35.
Final state: Answer 35
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
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
