[Set 234,256 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. We require root reduction in the steps. 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 234,256
(Answer is 484)
"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.
234,256 -> (23|42|56) : 23 is the 1st group number. The root digits is 2.
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Step 1: Place 234256 on CDEFGH
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Step 2: The 1st group is 23.
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Step 3: Square number ≦ 23 is 16=4^2. Place 4 on B as the 1st root.
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Step 4: Subtract 4^2 from the 1st group 23. Place 23-4^2=07 on CD.
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Step 5: Focus on 74256 on DEFGH.
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Step 6: Divide 74256 by 2. Place 37128 on DEFGH.
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Step 7: Divide 37 on DE by the current root 4.
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Step 8: 37/4=9 remainder 1. Place 9 on C as 2nd root.
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Step 9: Place remainder 01 on DEE.
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Step 10: Cannot subtract 9^2/2 from 11 on EF. 9 is excessive root. Place 9-1=8 on C.
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Step 11: Give back the current root 4 to E. Place 1+4=5 on E.
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Step 12: Subtract 2nd root^2/2 from 51 on EF. Place 51-8^2=19 on EF.
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Step 13: Divide 192 on EFG by the current root 48.
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Step 14: 192/48=4 remainder 0. Place 4 on D as 3rd root.
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Step 15: Place remainder 000 on EFG.
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Step 16: Focus on 8 on H.
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Step 17: Subtract 3rd root^2/2 from 8 on H. Place 0 on H.
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Step 18: Square root of 234256 is 484.
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Final state: Answer 484
Abacus state transition. (Click to Zoom)
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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
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. We require root reduction in the steps. 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 234,256
(Answer is 484)
"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.
234,256 -> (23|42|56) : 23 is the 1st group number. The root digits is 2.
Step 1: Place 234256 on CDEFGH
Step 2: The 1st group is 23.
Step 3: Square number ≦ 23 is 16=4^2. Place 4 on B as the 1st root.
Step 4: Subtract 4^2 from the 1st group 23. Place 23-4^2=07 on CD.
Step 5: Focus on 74256 on DEFGH.
Step 6: Divide 74256 by 2. Place 37128 on DEFGH.
Step 7: Divide 37 on DE by the current root 4.
Step 8: 37/4=9 remainder 1. Place 9 on C as 2nd root.
Step 9: Place remainder 01 on DEE.
Step 10: Cannot subtract 9^2/2 from 11 on EF. 9 is excessive root. Place 9-1=8 on C.
Step 11: Give back the current root 4 to E. Place 1+4=5 on E.
Step 12: Subtract 2nd root^2/2 from 51 on EF. Place 51-8^2=19 on EF.
Step 13: Divide 192 on EFG by the current root 48.
Step 14: 192/48=4 remainder 0. Place 4 on D as 3rd root.
Step 15: Place remainder 000 on EFG.
Step 16: Focus on 8 on H.
Step 17: Subtract 3rd root^2/2 from 8 on H. Place 0 on H.
Step 18: Square root of 234256 is 484.
Final state: Answer 484
Abacus state transition. (Click to Zoom)
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
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
