Square root 4,096 using abacus (Half-multiplication table method 1)

[Set 4,096 on Mr. Square root]

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[Japanese]

From this article, I begin to explain actual solutions how to calculate Square root using abacus. Today's example is simple - basic Half-multiplication table method (Hankuku 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.


Step 1: Place 4096 on CDEF.


Step 2: The 1st group is 40.


Step 3: Square number ≦ 40 is 36=6^2. Place 6 on B as the 1st root.


Step 4: Subtract 6^2 from the 1st group 40. 40-36=4


Step 5: Focus on 496 on DEF.


Step 6: Divide 496 by 2. Place 248 on DEF.


Step 7: Divide 24 on DE by the current root 6.


Step 8: 24/6=4 remainder 0. Place 4 on C as 2nd root.


Step 9: Place remainder 00 on DE.


Step 10: Focus on 8 in the 2nd group.


Step 11: Subtract half of the square of the 2nd root from 8. Place 8-4^2/2=0 on F.


Step 12: Square root of 4096 is 64.


Final state: Answer 64

Abacus state transition. (Click to Zoom)


It is interesting to compare with the Double-root method.


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

Square root 4,096 using abacus (Double-root method 1)
http://blog.goo.ne.jp/ktonegaw/e/fb902e129868386dd3162b9ff37af9a8


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