[Set 729 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 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: Set 729. 1st group is 7.
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Step 2: Square number less than or equal 7 is 4=2^2. 2 is the 1st root.
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Step 3: Subtract 2^2 from the 1st group 7. 7-4=3 : -a^2
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Step 4: Place 4 which is 2x of 1st root 2. This 4 is double root.
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Step 5: Focus on 32.
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Step 6: Divide 32 by 4. Answer=8 and this is 2nd root. : /2a
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Step 7: Subtract 4x8=32 from 32. : -2ab
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Step 8: You cannot subtract 8^2 (=64) from the 2nd group 9, so the 2nd root 8 is over-root. Subtract 1 from 2nd root8 then replace the 2nd root as 7, give back the double-root 4 to G.
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Step 9: Focus on 49.
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Step 10: Subtract 7^2 from 49 (GH) and set the answer 0 to GH.
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Step 11: Square root of 729 is 27.
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Final state: Answer 27
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 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: Set 729. 1st group is 7.
Step 2: Square number less than or equal 7 is 4=2^2. 2 is the 1st root.
Step 3: Subtract 2^2 from the 1st group 7. 7-4=3 : -a^2
Step 4: Place 4 which is 2x of 1st root 2. This 4 is double root.
Step 5: Focus on 32.
Step 6: Divide 32 by 4. Answer=8 and this is 2nd root. : /2a
Step 7: Subtract 4x8=32 from 32. : -2ab
Step 8: You cannot subtract 8^2 (=64) from the 2nd group 9, so the 2nd root 8 is over-root. Subtract 1 from 2nd root8 then replace the 2nd root as 7, give back the double-root 4 to G.
Step 9: Focus on 49.
Step 10: Subtract 7^2 from 49 (GH) and set the answer 0 to GH.
Step 11: Square root of 729 is 27.
Final state: Answer 27
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.
