[Set 11,943,936 on Mr. Square root]Zoom
[Japanese]
We will continue from where we ended in the last article, the actual solutions to calculate Square root using abacus. Today's example is Half-multiplication table method (Hankuku method), root is 4-digits case. Please check the Theory page for your reference. You can check the Index page of all articles.
Square root methods: Double-root method, Double-root alternative method, half-multiplication table method, half-multiplication table alternative method, multiplication-subtraction method, constant number method, etc.
Abacus steps to solve Square root of 11,943,936
(Answer is 3,456)
"1st group number" is the left most numbers in the 2-digits groups of the given number for square root calculation. Number of groups is the number of digits of the Square root.
11,943,936 -> (11|94|39|36) : 50 is the 1st group number. The root digits is 4.
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Step 1: Place 11943936 on CDEFGHIJ.
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Step 2: The 1st group is 11.
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Step 3: Square number ≦ 11 is 3=3^2. Place 3 on B as the 1st root.
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Step 4: Subtract 3^2 from the 1st group 11. Place 11-3^2=02 on CD.
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Step 5: Focus on 2943936 on DEFGHIJ.
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Step 6: Divide 2943936 by 2. Place 2943936/2=1471968 on DEFGHIJ.
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Step 7: Divide 14 on DE by the current root 3.
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Step 8: 14/3=4 remainder 2. Place 4 on C as 2nd root.
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Step 9: Place remainder 02 on DE.
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Step 10: Focus on 27 on EF.
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Step 11: Subtract 2nd root^2/2 from 27 on EF. Place 27-4^2=19 on EF.
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Step 12: Focus on 191 on EFG.
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Step 13: Divide 191 on EFG by the current root 34. 191/34=5 remainder 1.
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Step 14: Place 5 on D as 3rd root.
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Step 15: Place remainder 021 on EFG.
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Step 16: Focus on 19.6 on GHI.
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Step 17: Subtract 3rd root^2/2 from 19.6 on GHI. Place 021 on GHI.
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Step 18: Divide 2071 on FGHI by the current root 345. 2071/345=6 remainder 1.
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Step 19: Place 6 on E as 4th root.
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Step 20: Place remainder 0001 on FGHI.
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Step 21: Focus on 18 on IJ.
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Step 22: Subtract 3rd root^2/2 from 18 on IJ. Place 00 on IJ.
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Step 23: Square root of 11943936 is 3456.
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Final state: Answer 3456
Abacus state transition. (Click to Zoom)
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It is interesting to compare with the Double-root method.
Next article is solving Cube root by 1/3-multiplication table 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
Index: Square root and Cube root using Abacus
http://blog.goo.ne.jp/ktonegaw/e/f62fb31b6a3a0417ec5d33591249451b
Square root 11,943,936 using abacus (Double-root method 9)
http://blog.goo.ne.jp/ktonegaw/e/55a2c0aead038f4f140a77798ce8ff47
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
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[Japanese]
We will continue from where we ended in the last article, the actual solutions to calculate Square root using abacus. Today's example is Half-multiplication table method (Hankuku method), root is 4-digits case. Please check the Theory page for your reference. You can check the Index page of all articles.
Square root methods: Double-root method, Double-root alternative method, half-multiplication table method, half-multiplication table alternative method, multiplication-subtraction method, constant number method, etc.
Abacus steps to solve Square root of 11,943,936
(Answer is 3,456)
"1st group number" is the left most numbers in the 2-digits groups of the given number for square root calculation. Number of groups is the number of digits of the Square root.
11,943,936 -> (11|94|39|36) : 50 is the 1st group number. The root digits is 4.
Step 1: Place 11943936 on CDEFGHIJ.
Step 2: The 1st group is 11.
Step 3: Square number ≦ 11 is 3=3^2. Place 3 on B as the 1st root.
Step 4: Subtract 3^2 from the 1st group 11. Place 11-3^2=02 on CD.
Step 5: Focus on 2943936 on DEFGHIJ.
Step 6: Divide 2943936 by 2. Place 2943936/2=1471968 on DEFGHIJ.
Step 7: Divide 14 on DE by the current root 3.
Step 8: 14/3=4 remainder 2. Place 4 on C as 2nd root.
Step 9: Place remainder 02 on DE.
Step 10: Focus on 27 on EF.
Step 11: Subtract 2nd root^2/2 from 27 on EF. Place 27-4^2=19 on EF.
Step 12: Focus on 191 on EFG.
Step 13: Divide 191 on EFG by the current root 34. 191/34=5 remainder 1.
Step 14: Place 5 on D as 3rd root.
Step 15: Place remainder 021 on EFG.
Step 16: Focus on 19.6 on GHI.
Step 17: Subtract 3rd root^2/2 from 19.6 on GHI. Place 021 on GHI.
Step 18: Divide 2071 on FGHI by the current root 345. 2071/345=6 remainder 1.
Step 19: Place 6 on E as 4th root.
Step 20: Place remainder 0001 on FGHI.
Step 21: Focus on 18 on IJ.
Step 22: Subtract 3rd root^2/2 from 18 on IJ. Place 00 on IJ.
Step 23: Square root of 11943936 is 3456.
Final state: Answer 3456
Abacus state transition. (Click to Zoom)
It is interesting to compare with the Double-root method.
Next article is solving Cube root by 1/3-multiplication table 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
Index: Square root and Cube root using Abacus
http://blog.goo.ne.jp/ktonegaw/e/f62fb31b6a3a0417ec5d33591249451b
Square root 11,943,936 using abacus (Double-root method 9)
http://blog.goo.ne.jp/ktonegaw/e/55a2c0aead038f4f140a77798ce8ff47
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
