Square root 234,256 using abacus (Half-multiplication table method 5)

[Set 234,256 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. We require root reduction in the steps. 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 234,256
(Answer is 484)

"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.

234,256 -> (23|42|56) : 23 is the 1st group number. The root digits is 2.


Step 1: Place 234256 on CDEFGH


Step 2: The 1st group is 23.


Step 3: Square number ≦ 23 is 16=4^2. Place 4 on B as the 1st root.


Step 4: Subtract 4^2 from the 1st group 23. Place 23-4^2=07 on CD.


Step 5: Focus on 74256 on DEFGH.


Step 6: Divide 74256 by 2. Place 37128 on DEFGH.


Step 7: Divide 37 on DE by the current root 4.


Step 8: 37/4=9 remainder 1. Place 9 on C as 2nd root.


Step 9: Place remainder 01 on DEE.


Step 10: Cannot subtract 9^2/2 from 11 on EF. 9 is excessive root. Place 9-1=8 on C.


Step 11: Give back the current root 4 to E. Place 1+4=5 on E.


Step 12: Subtract 2nd root^2/2 from 51 on EF. Place 51-8^2=19 on EF.


Step 13: Divide 192 on EFG by the current root 48.


Step 14: 192/48=4 remainder 0. Place 4 on D as 3rd root.


Step 15: Place remainder 000 on EFG.


Step 16: Focus on 8 on H.


Step 17: Subtract 3rd root^2/2 from 8 on H. Place 0 on H.


Step 18: Square root of 234256 is 484.


Final state: Answer 484

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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