Square root 11,943,936 using abacus (Double-root method 9)

[Set 11,943,936 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 4-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 11,943,936
(Answer is 3,456)

"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.

11,943,936 -> (11|94|39|36) : 11 is the 1st group number. The root digits is 4.


Step 1: Set 11943936. 1st group is 11.


Step 2: Square number smaller than or equal to 11 is 9=3^2. 3 is the 1st root.


Step 3: Sbtract 3^2 from the 1st group 11. 11-9=02


Step 4: Focus on 29 on HI. Divide 29 by double root 6.


Step 5: Answer is 4. This is 2nd root on G. Place 29-6x4=05 on HI.


Step 6: Add 2x 2nd root 4=8 to double root. Focus o 54 on IJ.


Step 7: Subtract square of 2nd root 4 from 54 on IJ. Place 54-4^2=38 on IJ.


Step 8: Divide 383 on IJK by double root 68.


Step 9: Answer is 5. This is 3rd root on H.


Step 10: Place 383-68x5=043 on IJK.


Step 11: Add 2x 3rd root 5=10 to double root. Place 680+10=690 on ABC.


Step 12: Subtract square of 3rd root 5 from 439 on JKL. Place 439-5^2=414 on JKL.


Step 13: Divide 4143 on JKLM by double root 690.


Step 14: Answer is 6. This is 4th root on I.


Step 15: Place 4143-690x6=0003 on JKLM.


Step 16: Subtract square of 4th root 6 from 36 on MN.


Step 17: Place 36-6^2=00 on MN.


Step 18: Square root of 11943936 is 3456.


Final state: Answer 3456

Abacus state transition. (Click to Zoom)


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


Next article is about Cube root Theory (Triple-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 11,943,936 using abacus (Half-multiplication table method 8)
http://blog.goo.ne.jp/ktonegaw/e/a0394a9228e6d58cd4e48bf11a34a490


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