[Set 54,756 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 3-digits case basics. 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 54,756
(Answer is 234)
"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.
54,756 -> (05|47|56) : 5 is the 1st group number. The root digits is 2.
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Step 1: Place 54756 on DEFGH
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Step 2: The 1st group is 05.
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Step 3: Square number ≦ 5 is 4=2^2. Place 2 on B as the 1st root.
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Step 4: Subtract 2^2 from the 1st group 5. Place 5-2^2=08 on CD.
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Step 5: Focus on 14756 on DEFGH.
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Step 6: Divide 14756 by 2. Place 07378 on DEFGH.
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Step 7: Divide 7 on E by the current root 2.
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Step 8: 7/2=3 remainder 1. Place 3 on C as 2nd root.
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Step 9: Place remainder 1 on E.
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Step 10: Focus on 137 on EFG.
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Step 11: Subtract 2nd root^2/2 from 137 on EFG. Place 092 on EFG.
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Step 12: Divide 92 on FG by the current root 23.
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Step 13: 92/23=4 remainder 0. Place 4 on D as 3rd root.
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Step 14: Place remainder 00 on FG.
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Step 15: Focus on 8 on H.
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Step 16: Subtract 3rd root^2/2 from 8 on H. Place 0 on H.
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Step 17: Square root of 54756 is 234.
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Final state: Answer 234
Abacus state transition. (Click to Zoom)
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It is interesting to compare with the Double-root method.
Next article is also about Half-multiplication table method, more difficult example.
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 54,756 using abacus (Double-root method 5)
http://blog.goo.ne.jp/ktonegaw/e/0d0f5f4584c9b6c08376ae3bd3bf4a02
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 3-digits case basics. 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 54,756
(Answer is 234)
"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.
54,756 -> (05|47|56) : 5 is the 1st group number. The root digits is 2.
Step 1: Place 54756 on DEFGH
Step 2: The 1st group is 05.
Step 3: Square number ≦ 5 is 4=2^2. Place 2 on B as the 1st root.
Step 4: Subtract 2^2 from the 1st group 5. Place 5-2^2=08 on CD.
Step 5: Focus on 14756 on DEFGH.
Step 6: Divide 14756 by 2. Place 07378 on DEFGH.
Step 7: Divide 7 on E by the current root 2.
Step 8: 7/2=3 remainder 1. Place 3 on C as 2nd root.
Step 9: Place remainder 1 on E.
Step 10: Focus on 137 on EFG.
Step 11: Subtract 2nd root^2/2 from 137 on EFG. Place 092 on EFG.
Step 12: Divide 92 on FG by the current root 23.
Step 13: 92/23=4 remainder 0. Place 4 on D as 3rd root.
Step 14: Place remainder 00 on FG.
Step 15: Focus on 8 on H.
Step 16: Subtract 3rd root^2/2 from 8 on H. Place 0 on H.
Step 17: Square root of 54756 is 234.
Final state: Answer 234
Abacus state transition. (Click to Zoom)
It is interesting to compare with the Double-root method.
Next article is also about Half-multiplication table method, more difficult example.
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 54,756 using abacus (Double-root method 5)
http://blog.goo.ne.jp/ktonegaw/e/0d0f5f4584c9b6c08376ae3bd3bf4a02
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
