[Set 110,592 on Mr. Cube root]Zoom
[Japanese]
Following the last time, 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 and we require root reduction in the steps. 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 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: Place 110592 on GHIJKL.
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Step 2: The 1st group is 110.
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Step 3: Cube number ≦ 110 is 64=4^3. Place 4 on C as the 1st root.
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Step 4: Subtract 4^3 from the 1st group 110. Place 110-4^3=046 on GHI.
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Step 5: Focus on 46592 on HIJKL.
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Step 6: Divide 46592 by 3. Place 46592/3=15530.6 on HIJKLM.
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Step 7: Focus on 15 on HI.
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Step 8: Repeat division by triple root 4 until 4th digits next to 1st root. 15/4=3 remainder 3. Place 3 on E.
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Step 9: Place remainder 03 on HI.
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Step 10: Divide 35 on IJ by current root 4. 35/4=8 remainder 3
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Step 11: Place 8 on F.
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Step 12: Place 03 on IJ.
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Step 13: Divide 33 on JK by current root 4. 33/4=8 remainder 1
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Step 14: Place 8 on G.
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Step 15: Place 01 on JK.
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Step 16: Divide 38 on EF by current root 4. 38/4=9 remainder 2
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Step 17: Place 9 on D as 2nd root. (Temporary root)
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Step 18: Place 02 on EF.
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Step 19: Cannot subtract 9^2=81 from 28. Temporary root 9 is excessive root.
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Step 20: Subtract 1 from excessive root 9. Place 8 on D.
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Step 21: Return current root 2 on E. Place 2+4=6 on F.
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Step 22: Place 68-2nd root^2=68-8^2=04 on FG.
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Step 23: 04 on FG x 1st root 4 + 01 on JK. Place 4x4+1=17 on JK.
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Step 24: Subtract 2nd root 8^3/3 from 176 on KLM. 176-8^3/3=0
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Step 25: Place 000 on KLM.
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Step 26: Cube root of 110592 is 48.
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Final state: Answer 48
Abacus state transition. (Click to Zoom)
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It is interesting to compare with the Triple-root method.
Next article is also 1/3-multiplication table method.
Related articles:
How to solve Cube root of 1729.03 using abacus? (Feynman v.s. Abacus man)
https://blog.goo.ne.jp/ktonegaw/e/cff5d6e7ecaa07230b9cc7af10b23aed
Index: Square root and Cube root using Abacus
https://blog.goo.ne.jp/ktonegaw/e/f62fb31b6a3a0417ec5d33591249451b
Cube root 110,592 using abacus (Triple-root method 3)
https://blog.goo.ne.jp/ktonegaw/e/ca623f02e6f5fdfef4221a5c43ea1a95
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[Japanese]
Following the last time, 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 and we require root reduction in the steps. 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 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: Place 110592 on GHIJKL.
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Step 2: The 1st group is 110.
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Step 3: Cube number ≦ 110 is 64=4^3. Place 4 on C as the 1st root.
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Step 4: Subtract 4^3 from the 1st group 110. Place 110-4^3=046 on GHI.
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Step 5: Focus on 46592 on HIJKL.
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Step 6: Divide 46592 by 3. Place 46592/3=15530.6 on HIJKLM.
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Step 7: Focus on 15 on HI.
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Step 8: Repeat division by triple root 4 until 4th digits next to 1st root. 15/4=3 remainder 3. Place 3 on E.
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Step 9: Place remainder 03 on HI.
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Step 10: Divide 35 on IJ by current root 4. 35/4=8 remainder 3
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Step 11: Place 8 on F.
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Step 12: Place 03 on IJ.
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Step 13: Divide 33 on JK by current root 4. 33/4=8 remainder 1
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Step 14: Place 8 on G.
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Step 15: Place 01 on JK.
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Step 16: Divide 38 on EF by current root 4. 38/4=9 remainder 2
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Step 17: Place 9 on D as 2nd root. (Temporary root)
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Step 18: Place 02 on EF.
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Step 19: Cannot subtract 9^2=81 from 28. Temporary root 9 is excessive root.
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Step 20: Subtract 1 from excessive root 9. Place 8 on D.
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Step 21: Return current root 2 on E. Place 2+4=6 on F.
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Step 22: Place 68-2nd root^2=68-8^2=04 on FG.
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Step 23: 04 on FG x 1st root 4 + 01 on JK. Place 4x4+1=17 on JK.
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Step 24: Subtract 2nd root 8^3/3 from 176 on KLM. 176-8^3/3=0
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Step 25: Place 000 on KLM.
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Step 26: Cube root of 110592 is 48.
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Final state: Answer 48
Abacus state transition. (Click to Zoom)
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It is interesting to compare with the Triple-root method.
Next article is also 1/3-multiplication table method.
Related articles:
How to solve Cube root of 1729.03 using abacus? (Feynman v.s. Abacus man)
https://blog.goo.ne.jp/ktonegaw/e/cff5d6e7ecaa07230b9cc7af10b23aed
Index: Square root and Cube root using Abacus
https://blog.goo.ne.jp/ktonegaw/e/f62fb31b6a3a0417ec5d33591249451b
Cube root 110,592 using abacus (Triple-root method 3)
https://blog.goo.ne.jp/ktonegaw/e/ca623f02e6f5fdfef4221a5c43ea1a95
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
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