[Set 729 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 2-digits case. We require root reduction in the steps. Please check the Theory page for your reference.
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 729 (Answer is 27)
"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.
729 -> (07|29) : 07 is the 1st group number. The root digits is 2.
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Step 1: Place 729 on DEF.
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Step 2: The 1st group is 7.
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Step 3: Square number ≦ 7 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 7. Place 7-2^2=3 on D.
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Step 5: Focus on 329 on DEF.
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Step 6: Divide 329 by 2. Place 1645 on DEFG.
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Step 7: Divide 16 on DE by the current root 2.
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Step 8: 16/2=8 remainder 0. Place 2 on C as 2nd root.
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Step 9: Place remainder 00 on DE.
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Step 10: Subtract half of the square of the 2nd root from 8. But 8-4^2/2 is minus. The 2nd root 8 is excessive root.
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Step 11: Subtract 1 from the excessive root 8. Place 7 as 2nd root. Return 1x current root 2 on E.
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Step 12: Focus on 245 on EFG.
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Step 13: Subtract 2nd root^2/2 from 245 on EFG. Place 000 on EFG.
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Step 14: Square root of 729 is 27.
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Final state: Answer 27
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 729 using abacus (Double-root method 3)
http://blog.goo.ne.jp/ktonegaw/e/d11c31bd52c957a4e1cdb7f502af8b76
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 2-digits case. We require root reduction in the steps. Please check the Theory page for your reference.
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 729 (Answer is 27)
"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.
729 -> (07|29) : 07 is the 1st group number. The root digits is 2.
Step 1: Place 729 on DEF.
Step 2: The 1st group is 7.
Step 3: Square number ≦ 7 is 4=2^2. Place 2 on B as the 1st root.
Step 4: Subtract 2^2 from the 1st group 7. Place 7-2^2=3 on D.
Step 5: Focus on 329 on DEF.
Step 6: Divide 329 by 2. Place 1645 on DEFG.
Step 7: Divide 16 on DE by the current root 2.
Step 8: 16/2=8 remainder 0. Place 2 on C as 2nd root.
Step 9: Place remainder 00 on DE.
Step 10: Subtract half of the square of the 2nd root from 8. But 8-4^2/2 is minus. The 2nd root 8 is excessive root.
Step 11: Subtract 1 from the excessive root 8. Place 7 as 2nd root. Return 1x current root 2 on E.
Step 12: Focus on 245 on EFG.
Step 13: Subtract 2nd root^2/2 from 245 on EFG. Place 000 on EFG.
Step 14: Square root of 729 is 27.
Final state: Answer 27
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 729 using abacus (Double-root method 3)
http://blog.goo.ne.jp/ktonegaw/e/d11c31bd52c957a4e1cdb7f502af8b76
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
