[Set 54,756 on Mr. Square root]Zoom
[Japanese]
We will continue from where we ended in the last article, the article shows actual solutions to calculate Square root using abacus. Today's example is simple - basic Double-root method, root is 3-digits case. 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 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 3.
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Step 1: Set 54756. 1st group is 5.
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Step 2: Square number equal to or smaller than 5 is 4=2^2. 2 is the 1st root. Place 4 which is 2x of 1st root 2. This 4 is double root.
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Step 3: Subtract 2^2 from the 1st group 5. 5-4=1 : -a^2
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Step 4: Focus on 14 and divide it by double root 4.
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Step 5: Answer=3 and this is 2nd root. Set second root 3 on E.
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Step 6: Subtract double root 4 x 2nd root 3 from 14. 14-4x3=02.
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Step 7: Focus on 27.
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Step 8: Subtract (2nd root 3)^2 from 2nd group 27. 27-3^2=18
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Step 9: Add 2x2nd root 3 to double root. Set 2x3=6 on B.
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Step 10: Focus on double root 46 and 185.
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Step 11: Divide 185 by double root 46. Answer=4 reminder 1. Set them on F and I.
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Step 12: Subtract (3rd root 4)^2 from 3rd group 16. 16–4^2 =0: -b^2
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Step 13: Square root of 54756 is 234.
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Final state: Answer 234
Abacus state transition. (Click to Zoom)
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Next article is also about Double-root 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
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[Japanese]
We will continue from where we ended in the last article, the article shows actual solutions to calculate Square root using abacus. Today's example is simple - basic Double-root method, root is 3-digits case. 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 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 3.
Step 1: Set 54756. 1st group is 5.
Step 2: Square number equal to or smaller than 5 is 4=2^2. 2 is the 1st root. Place 4 which is 2x of 1st root 2. This 4 is double root.
Step 3: Subtract 2^2 from the 1st group 5. 5-4=1 : -a^2
Step 4: Focus on 14 and divide it by double root 4.
Step 5: Answer=3 and this is 2nd root. Set second root 3 on E.
Step 6: Subtract double root 4 x 2nd root 3 from 14. 14-4x3=02.
Step 7: Focus on 27.
Step 8: Subtract (2nd root 3)^2 from 2nd group 27. 27-3^2=18
Step 9: Add 2x2nd root 3 to double root. Set 2x3=6 on B.
Step 10: Focus on double root 46 and 185.
Step 11: Divide 185 by double root 46. Answer=4 reminder 1. Set them on F and I.
Step 12: Subtract (3rd root 4)^2 from 3rd group 16. 16–4^2 =0: -b^2
Step 13: Square root of 54756 is 234.
Final state: Answer 234
Abacus state transition. (Click to Zoom)
Next article is also about Double-root 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
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
