Square root 54,756 using abacus (Double-root method 5)

[Set 54,756 on Mr. Square root]

Zoom

[Japanese]

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 3-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 54,756 (Answer is 234)

"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.

54,756 -> (05|47|56) : 5 is the 1st group number. The root digits is 3.


Step 1: Set 54756. 1st group is 5.


Step 2: Square number equal to or smaller than 5 is 4=2^2. 2 is the 1st root. Place 4 which is 2x of 1st root 2. This 4 is double root.


Step 3: Subtract 2^2 from the 1st group 5. 5-4=1 : -a^2


Step 4: Focus on 14 and divide it by double root 4.


Step 5: Answer=3 and this is 2nd root. Set second root 3 on E.


Step 6: Subtract double root 4 x 2nd root 3 from 14. 14-4x3=02.


Step 7: Focus on 27.


Step 8: Subtract (2nd root 3)^2 from 2nd group 27. 27-3^2=18


Step 9: Add 2x2nd root 3 to double root. Set 2x3=6 on B.


Step 10: Focus on double root 46 and 185.


Step 11: Divide 185 by double root 46. Answer=4 reminder 1. Set them on F and I.


Step 12: Subtract (3rd root 4)^2 from 3rd group 16. 16–4^2 =0: -b^2


Step 13: Square root of 54756 is 234.


Final state: Answer 234

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.


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 54,756 using abacus (Half-multiplication table method 4)
http://blog.goo.ne.jp/ktonegaw/e/1b44b7ed25f245921ba9546048c2e676


Please place your mouse on the buttons and click one by one. These are blog ranking sites.