Square root 4,761 using abacus (Double-root method 4)

[Set 4,761 on Mr. Square root]

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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 9 as root in the middle of calculation. 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 4,761 (Answer is 69)

"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.

4761 -> (47|61) : 47 is the 1st group number. The root digits is 2.


Step 1: Set 4761. 1st group is 47.


Step 2: Square number equal to or smaller than 47 is 36=6^2. 6 is the 1st root. Place 12 which is 2x of 1st root 6. This 12 is double root.


Step 3: Subtract 6^2 from the 1st group 47. 47-36=11 : -a^2


Step 4: Focus on 116 and divide it by 12.


Step 5: Answer=9 and this is 2nd root. : /2a, Set 116-9x12=008 on EFG.


Step 6: Subtract 9^2=81 from 2nd group 81. 81-81=0 : -b^2


Step 7: Square root of 4761 is 69.


Final state: Answer 69

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

Index: Square root and Cube root using Abacus
http://blog.goo.ne.jp/ktonegaw/e/f62fb31b6a3a0417ec5d33591249451b


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