[Set 59,319 on Mr. Cube root]Zoom
[Japanese]
Today's example is also about actual solution of Cube root using abacus. The calculation becomes more complicated than previous example.
Today's example is simple - basic Triple-root method, root is 2-digits case and we require 9 as root in the steps. Please check the Theory page for your reference.
Cube root methods: Triple-root method, constant number method, 3a^2 method, 1/3-division method, 1/3-multiplication table method, 1/3-multiplication table alternative method, Multiplication-Subtraction method, 3-root^2 method, Mixing method, Exceed number method, Omission Method, etc.
Abacus steps to solve Square root of 59,319
(Answer is 39)
"1st group number" is the left most numbers in the 3-digits groups of the given number for cube root calculation. Number of groups is the number of digits of the Cube root.
59,319 -> (59|319) : 59 is the 1st group number. The root digits is 2.
![]()
Step 1: Set 59319. First group is 59.
![]()
Step 2: Cube number smaller than 59 is 27=3^3. Place 3 on E as 1st root.
![]()
Step 3: Place 59-27=32 on HI. (-a^3)
![]()
Step 4: Place Triple root 3x3=9 on B.
![]()
Step 5: Repeat division by triple root 9 until 4th digits next to 1st root. (÷3a)
![]()
Step 6: 32/9=3 remainder 5. Place 3 on G.
![]()
Step 7: Place remainder 05 on HI.
![]()
Step 8: 53/9=5 remainder 8. Place 5 on H.
![]()
Step 9: Place remainder 08 on IJ.
![]()
Step 10: 81/9=9 remainder 0.
![]()
Step 11: Place remainder 00 on JK.
![]()
Step 12: As the last digit of triple root B equals to the last digit of remaining root I, we set 9 on F as 2nd root.
![]()
Step 13: 35/9=3 remainder 8. (-b^2)
![]()
Step 14: Place remainder 08 on GH.
![]()
Step 15: Focus on 89.
![]()
Step 16: Place 89-2nd root^2=89-9^2=08 on HI.
![]()
Step 17: Multiply triple root B by remainder of the square subtraction 08. Place 08x9=72 on JK.
![]()
Step 18: Subtract 2nd root^3 from 729. (-b^3)
![]()
Step 19: Place 729-9^3=000 on JKL.
![]()
Step 20: Cube root of 59319 is 39.
![]()
Final state: Answer 39
Abacus state transition. (Click to Zoom)
![]()
Next article is also about Cube root calculation (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
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
![にほんブログ村 科学ブログ 物理学へ]()
![人気ブログランキングへ]()
![]()
[Japanese]
Today's example is also about actual solution of Cube root using abacus. The calculation becomes more complicated than previous example.
Today's example is simple - basic Triple-root method, root is 2-digits case and we require 9 as root in the steps. Please check the Theory page for your reference.
Cube root methods: Triple-root method, constant number method, 3a^2 method, 1/3-division method, 1/3-multiplication table method, 1/3-multiplication table alternative method, Multiplication-Subtraction method, 3-root^2 method, Mixing method, Exceed number method, Omission Method, etc.
Abacus steps to solve Square root of 59,319
(Answer is 39)
"1st group number" is the left most numbers in the 3-digits groups of the given number for cube root calculation. Number of groups is the number of digits of the Cube root.
59,319 -> (59|319) : 59 is the 1st group number. The root digits is 2.
Step 1: Set 59319. First group is 59.
Step 2: Cube number smaller than 59 is 27=3^3. Place 3 on E as 1st root.
Step 3: Place 59-27=32 on HI. (-a^3)
Step 4: Place Triple root 3x3=9 on B.
Step 5: Repeat division by triple root 9 until 4th digits next to 1st root. (÷3a)
Step 6: 32/9=3 remainder 5. Place 3 on G.
Step 7: Place remainder 05 on HI.
Step 8: 53/9=5 remainder 8. Place 5 on H.
Step 9: Place remainder 08 on IJ.
Step 10: 81/9=9 remainder 0.
Step 11: Place remainder 00 on JK.
Step 12: As the last digit of triple root B equals to the last digit of remaining root I, we set 9 on F as 2nd root.
Step 13: 35/9=3 remainder 8. (-b^2)
Step 14: Place remainder 08 on GH.
Step 15: Focus on 89.
Step 16: Place 89-2nd root^2=89-9^2=08 on HI.
Step 17: Multiply triple root B by remainder of the square subtraction 08. Place 08x9=72 on JK.
Step 18: Subtract 2nd root^3 from 729. (-b^3)
Step 19: Place 729-9^3=000 on JKL.
Step 20: Cube root of 59319 is 39.
Final state: Answer 39
Abacus state transition. (Click to Zoom)
Next article is also about Cube root calculation (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
Please place your mouse on the buttons and click one by one. These are blog ranking sites.
