[Set 323,761 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. We require 9 as root in the middle of calculation. 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 323,761
(Answer is 569)
"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.
323761 -> (32|37|61) : 32 is the 1st group number. The root digits is 3.
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Step 1: Set 323761. 1st group is 32.。
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Step 2: Square number smaller than or equal to 32 is 25=5^2. 5 is the 1st root.
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Step 3: Subtract 5^2 from the 1st group 32. 32-25=07
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Step 4: Place 10 which is 2x of 1st root 5. This 10 is double root. Focus on 73.
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Step 5: Divide 73 by 10. Answer=6 and this is 2nd root. Subtract 10x6 from 73. 73-10x6=13
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Step 6: Place 2x double root 12 on BC. Focus on 37.
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Step 7: Subtract 6^2 from 37. 37-6x6=01。
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Step 8: Focus on 2nd root 8 and 131 on FGH.
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Step 9: Divide 1016 by 12. Answer=9. 9 is the 3rd root on G.
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Step 10: Set 1016-112x9=0008 on HIJK.
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Step 11: Focus on 3rd root 9 and 81 on KL.
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Step 12: Subtract 9^2 from 81 on KL. Set 81-81=00 on KL.
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Step 13: Square root of 323761 is 569.
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Final state: Answer 569
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. We require 9 as root in the middle of calculation. 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 323,761
(Answer is 569)
"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.
323761 -> (32|37|61) : 32 is the 1st group number. The root digits is 3.
Step 1: Set 323761. 1st group is 32.。
Step 2: Square number smaller than or equal to 32 is 25=5^2. 5 is the 1st root.
Step 3: Subtract 5^2 from the 1st group 32. 32-25=07
Step 4: Place 10 which is 2x of 1st root 5. This 10 is double root. Focus on 73.
Step 5: Divide 73 by 10. Answer=6 and this is 2nd root. Subtract 10x6 from 73. 73-10x6=13
Step 6: Place 2x double root 12 on BC. Focus on 37.
Step 7: Subtract 6^2 from 37. 37-6x6=01。
Step 8: Focus on 2nd root 8 and 131 on FGH.
Step 9: Divide 1016 by 12. Answer=9. 9 is the 3rd root on G.
Step 10: Set 1016-112x9=0008 on HIJK.
Step 11: Focus on 3rd root 9 and 81 on KL.
Step 12: Subtract 9^2 from 81 on KL. Set 81-81=00 on KL.
Step 13: Square root of 323761 is 569.
Final state: Answer 569
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.
