Square root 501,264 using abacus (Half-multiplication table method 7)

[Set 501,264 on Mr. Square root]

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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 3-digits case and contains Zero. Please check the Theory page for your reference. You can check the Index page of all articles.

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 501,264
(Answer is 708)

"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.

501,264 -> (50|12|64) : 50 is the 1st group number. The root digits is 3.


Step 1: Place 501264 on CDEFGH.


Step 2: The 1st group is 50.


Step 3: Square number ≦ 50 is 49=7^2. Place 7 on B as the 1st root.


Step 4: Subtract 7^2 from the 1st group 50. Place 50-7^2=01 on CD.


Step 5: Focus on 11264 on DEFGH.


Step 6: Divide 11264 by 2. Place 11264/2=05632 on DEFGH.


Step 7: Divide 05 on DE by the current root 7.


Step 8: Cannot divide. Place 0 on C as 2nd root.


Step 9: Divide 563 on EFG by the current root 70. 563/70=8 remainder 3


Step 10: Place 8 on D as 3rd root.


Step 11: Place remainder 003 on EFG.


Step 12: Focus on 32 on GH.


Step 13: Subtract 3rd root^2/2 from 32 on GH. Place 00 on GH.


Step 14: Square root of 501264 is 708.


Final state: Answer 708

Abacus state transition. (Click to Zoom)



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


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