[Set 385,828,352 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 3-digits case. 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 385,828,352
(Answer is 728)
"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.
385,828,352 -> (385|828|352) : 385 is the 1st group number. The root digits is 3.
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Step 1: Set 385828352. First group is 385.
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Step 2: Cube number smaller than 385 is 343=7^3. Place 7 on D as 1st root.
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Step 3: Place 385-343=042 on GHI. (-a^3)
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Step 4: Place Triple root 3x7=21 on AB.
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Step 5: Repeat division by triple root 21 until 4th digits next to 1st root. (÷3a)
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Step 6: 42/21=2 remainder 0. Place 2 on F.
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Step 7: Place remainder 00 on HI.
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Step 8: 82/21=3 remainder 19.
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Step 9: Place 3 on H.
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Step 10: Place remainder 19 on JK.
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Step 11: Divide 20 on FG by current root 7. 20/7=2 remainder 6.
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Step 12: Place 2 E as 2nd root.
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Step 13: Place remainder 06 on FG.
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Step 14: Subtract 2nd root^2 from 63 on GH. (-b^2)
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Step 15: Place 63-2^2=59 on GH.
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Step 16: Multiply triple root 21 by remainder 59 on GH. 21X59=1239
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Step 17: Replace 59 by 00 on GH.
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Step 18: Add 1239 to 0019 on HIJK.
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Step 19: It means place 0019+1239=1258 on HIJK.
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Step 20: Subtract 2nd root^3 from 8 on L. (-b^3)
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Step 21: It means place 8-2^3=0 on L.
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Step 22: Add 3x2nd root to triple root root on ABC. It means place 3x2=6 on C.
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Step 23: Repeat division by triple root 216 until 4th digits next to 1st root. (÷3a)
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Step 24: Divide 1258 on HIJK by triple root 216. Place 1258/216=5 remainder 178. Place 5 on G.
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Step 25: Place 0178 on HIJK.
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Step 26: 1780/216=8 remainder 52
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Step 27: Place 8 on H.
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Step 28: Place remainder 0052 on IJKL.
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Step 29: 523/216=2 remainder 91
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Step 30: Place 2 on I.
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Step 31: Place remainder 091 on KLM.
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Step 32: 915/216=4 remainder 51
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Step 33: Place 4 on J.
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Step 34: Place remainder 051 on LMN.
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Step 35: Divide 582 by current root 72.
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Step 36: 582/72=8 remainder 6. Place 8 on F as 3rd root.
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Step 37: Place remainder 006 on GHI.
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Step 38: Subtract 3rd root^2 from 64 on IJ. (-c^2)
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Step 39: Place 64-8^2=00 on IJ.
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Step 40: Subtract 3rd root^3 from 512 on MNO. (-c^3)
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Step 41: Place 512-8^3=000 on MNO.
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Step 42: Cube root of 385828352 is 728.
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Final state: Answer 728
Abacus state transition. (Click to Zoom)
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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
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[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 3-digits case. 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 385,828,352
(Answer is 728)
"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.
385,828,352 -> (385|828|352) : 385 is the 1st group number. The root digits is 3.
Step 1: Set 385828352. First group is 385.
Step 2: Cube number smaller than 385 is 343=7^3. Place 7 on D as 1st root.
Step 3: Place 385-343=042 on GHI. (-a^3)
Step 4: Place Triple root 3x7=21 on AB.
Step 5: Repeat division by triple root 21 until 4th digits next to 1st root. (÷3a)
Step 6: 42/21=2 remainder 0. Place 2 on F.
Step 7: Place remainder 00 on HI.
Step 8: 82/21=3 remainder 19.
Step 9: Place 3 on H.
Step 10: Place remainder 19 on JK.
Step 11: Divide 20 on FG by current root 7. 20/7=2 remainder 6.
Step 12: Place 2 E as 2nd root.
Step 13: Place remainder 06 on FG.
Step 14: Subtract 2nd root^2 from 63 on GH. (-b^2)
Step 15: Place 63-2^2=59 on GH.
Step 16: Multiply triple root 21 by remainder 59 on GH. 21X59=1239
Step 17: Replace 59 by 00 on GH.
Step 18: Add 1239 to 0019 on HIJK.
Step 19: It means place 0019+1239=1258 on HIJK.
Step 20: Subtract 2nd root^3 from 8 on L. (-b^3)
Step 21: It means place 8-2^3=0 on L.
Step 22: Add 3x2nd root to triple root root on ABC. It means place 3x2=6 on C.
Step 23: Repeat division by triple root 216 until 4th digits next to 1st root. (÷3a)
Step 24: Divide 1258 on HIJK by triple root 216. Place 1258/216=5 remainder 178. Place 5 on G.
Step 25: Place 0178 on HIJK.
Step 26: 1780/216=8 remainder 52
Step 27: Place 8 on H.
Step 28: Place remainder 0052 on IJKL.
Step 29: 523/216=2 remainder 91
Step 30: Place 2 on I.
Step 31: Place remainder 091 on KLM.
Step 32: 915/216=4 remainder 51
Step 33: Place 4 on J.
Step 34: Place remainder 051 on LMN.
Step 35: Divide 582 by current root 72.
Step 36: 582/72=8 remainder 6. Place 8 on F as 3rd root.
Step 37: Place remainder 006 on GHI.
Step 38: Subtract 3rd root^2 from 64 on IJ. (-c^2)
Step 39: Place 64-8^2=00 on IJ.
Step 40: Subtract 3rd root^3 from 512 on MNO. (-c^3)
Step 41: Place 512-8^3=000 on MNO.
Step 42: Cube root of 385828352 is 728.
Final state: Answer 728
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.
