Square root 4,096 using abacus (Double-root method 1)

[Set 4,096 on Mr. Square root]

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From this article, I begin to explain actual solutions how to calculate Square root using abacus. Today's example is simple - basic Double-root 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: Set 4096. 1st group is 40.


Step 2: Square number less than or equal 40 is 36=6^2. 6 is the 1st root.


Step 3: Subtract 6^2 from the 1st group 40. 40-36=4 : -a^2


Step 4: Place 12 which is 2x of 1st root 6. This 12 is double root.


Step 5: Divide 496 by 12. Answer=4 and this is 2nd root. : /2a


Step 6: Subtract 4x12=48 from 49. : -2ab


Step 7: Subtract 4^2=16 from 2nd group 16. 16-16=0 : -b^2


Step 8: Square root of 4096 is 64.


Final state: Answer 64

Abacus state transition. (Click to Zoom)


It is interesting to compare with the Half-multiplication table method.


Next article is also about Double-root 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 (Half-multiplication table method 1)
http://blog.goo.ne.jp/ktonegaw/e/276950d85e47805be2501f3e41301332


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