[Set 4,096 on Mr. Square root]Zoom
[Japanese]
From this article, I begin to explain actual solutions how to calculate Square root using abacus. Today's example is simple - basic Double-root method, root is 2-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 4,096 (Answer is 64)
"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.
4,096 -> (40|96) : 40 is the 1st group number. The root digits is 2.
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Step 1: Set 4096. 1st group is 40.
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Step 2: Square number less than or equal 40 is 36=6^2. 6 is the 1st root.
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Step 3: Subtract 6^2 from the 1st group 40. 40-36=4 : -a^2
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Step 4: Place 12 which is 2x of 1st root 6. This 12 is double root.
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Step 5: Divide 496 by 12. Answer=4 and this is 2nd root. : /2a
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Step 6: Subtract 4x12=48 from 49. : -2ab
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Step 7: Subtract 4^2=16 from 2nd group 16. 16-16=0 : -b^2
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Step 8: Square root of 4096 is 64.
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Final state: Answer 64
Abacus state transition. (Click to Zoom)
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Next article is also about Double-root 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
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
Image may be NSFW.
Clik here to view. Image may be NSFW.
Clik here to view. Image may be NSFW.
Clik here to view.
[Japanese]
From this article, I begin to explain actual solutions how to calculate Square root using abacus. Today's example is simple - basic Double-root method, root is 2-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 4,096 (Answer is 64)
"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.
4,096 -> (40|96) : 40 is the 1st group number. The root digits is 2.
Image may be NSFW.
Clik here to view.
Step 1: Set 4096. 1st group is 40.
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Step 2: Square number less than or equal 40 is 36=6^2. 6 is the 1st root.
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Clik here to view.
Step 3: Subtract 6^2 from the 1st group 40. 40-36=4 : -a^2
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Clik here to view.
Step 4: Place 12 which is 2x of 1st root 6. This 12 is double root.
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Step 5: Divide 496 by 12. Answer=4 and this is 2nd root. : /2a
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Step 6: Subtract 4x12=48 from 49. : -2ab
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Step 7: Subtract 4^2=16 from 2nd group 16. 16-16=0 : -b^2
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Step 8: Square root of 4096 is 64.
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Final state: Answer 64
Abacus state transition. (Click to Zoom)
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Clik here to view.
Next article is also about Double-root 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
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
Image may be NSFW.
Clik here to view.
Image may be NSFW.Clik here to view.
Image may be NSFW.Clik here to view.
