[Set 2,401 on Mr. Square root]
[Japanese]
We will continue from where we ended in the last article, the actual solutions to calculate Square root using abacus. Today's example is Half-multiplication table method (Hankuku method), root is 2-digits case. We require 9 as root in the middle of calculation. Please check the Theory page for your reference. You can check the Index page of all articles.
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 2,401 (Answer is 49)
"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.
2,401 -> (24|01) : 24 is the 1st group number. The root digits is 2.
Step 1: Place 2401 on CDEF.
Step 2: The 1st group is 24.
Step 3: Square number ≦ 24 is 16=4^2. Place 4 on B as the 1st root.
Step 4: Subtract 4^2 from the 1st group 24. Place 24-4^2=08 on CD.
Step 5: Focus on 801 on DEF.
Step 6: Divide 801 by 2. Place 4005 on DEFG.
Step 7: Divide 40 on DE by the current root 4.
Step 8: 40/4=9 remainder 4. Place 9 on C as 2nd root.
Step 9: Place remainder 04 on DE.
Step 10: Focus on 405 on EFG.
Step 11: Subtract 2nd root^2/2 from 405 on EFG. Place 000 on EFG.
Step 12: Square root of 2401 is 49.
Final state: Answer 49
Abacus state transition. (Click to Zoom)
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
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