[Set 110,592 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 we require root reduction in the steps 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 110,592
(Answer is 48)
"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.
110,592 -> (110|592) : 110 is the 1st group number. The root digits is 2.
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Step 1: Set 110592. First group is 110.
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Step 2: Cube number smaller than 110 is 64=4^3. Place 4 on D as 1st root.
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Step 3: Place 110-64=046 on GHI. (-a^3)
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Step 4: Place Triple root 3x4=12 on AB.
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Step 5: Repeat division by triple root 12 until 4th digits next to 1st root. (÷3a)
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Step 6: 46/12=3 remainder 10. Place 3 on F.
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Step 7: Place remainder 10 on HI.
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Step 8: 105/12=8 remainder 9. Place 8 on G.
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Step 9: Place remainder 009 on HIJ.
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Step 10: 99/12=8 remainder 3 Place 8 on H.
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Step 11: Place remainder 03 on JK.
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Step 12: Divide 38 by current root (1st root) 4.(÷a)
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Step 13: Answer is 9 and place 9 on E as 2nd root (temporary root).
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Step 14: Cannot subtract 9^2=81 from 28. Temporary root 9 is excessive root.
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Step 15: Subtract 1 from excessive root 9. Place 8 on E.
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Step 16: Place 26-2nd root^2=26-5^2=01 on HI.
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Step 17: Place 68-2nd root^2=68-8^2=04 on GH. (-b^2)
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Step 18: Add 12x(remainder 04) to 03 on JK.
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Step 19: Place 04x12+03=51 on JK.
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Step 20: Subtract 2nd root^3 from 512. (-b^3)
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Step 21: Place 512-8^3=000 on JKL.
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Step 22: Cube root of 110592 is 48.
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Final state: Answer 48
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 we require root reduction in the steps 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 110,592
(Answer is 48)
"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.
110,592 -> (110|592) : 110 is the 1st group number. The root digits is 2.
Step 1: Set 110592. First group is 110.
Step 2: Cube number smaller than 110 is 64=4^3. Place 4 on D as 1st root.
Step 3: Place 110-64=046 on GHI. (-a^3)
Step 4: Place Triple root 3x4=12 on AB.
Step 5: Repeat division by triple root 12 until 4th digits next to 1st root. (÷3a)
Step 6: 46/12=3 remainder 10. Place 3 on F.
Step 7: Place remainder 10 on HI.
Step 8: 105/12=8 remainder 9. Place 8 on G.
Step 9: Place remainder 009 on HIJ.
Step 10: 99/12=8 remainder 3 Place 8 on H.
Step 11: Place remainder 03 on JK.
Step 12: Divide 38 by current root (1st root) 4.(÷a)
Step 13: Answer is 9 and place 9 on E as 2nd root (temporary root).
Step 14: Cannot subtract 9^2=81 from 28. Temporary root 9 is excessive root.
Step 15: Subtract 1 from excessive root 9. Place 8 on E.
Step 16: Place 26-2nd root^2=26-5^2=01 on HI.
Step 17: Place 68-2nd root^2=68-8^2=04 on GH. (-b^2)
Step 18: Add 12x(remainder 04) to 03 on JK.
Step 19: Place 04x12+03=51 on JK.
Step 20: Subtract 2nd root^3 from 512. (-b^3)
Step 21: Place 512-8^3=000 on JKL.
Step 22: Cube root of 110592 is 48.
Final state: Answer 48
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.
