Index: Square root and Cube root using Abacus

Square root and Cube root

[Japanese]

Many a little drop of water makes an ocean. Accumulation of small efforts may bring something valuable.

The index page is useful to search solution. I will add the article entry point from now on.

There are pages and books about Square and Cube root solution using abacus. But they contains few solution methods and omit detail calculation steps.

This is the world's first solution library for 1) Many solution methods, 2) Covering many calculation patterns and 3) Showing calculation steps in detail.


Square root calculation



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.

Double-root method (Baikon method)
Open: Double-root method Theory
Open: Square root of 4,096, Basics
Open: Square root of 1,225, Basics
Open: Square root of 729, require root reduction in the steps.
Open: Square root of 4,761, require 9 as root in the middle of calculation.
Open: Square root of 54,756, 3 digits root Basics
Open: Square root of 237,169, 3 digits root, require root reduction in the steps
Open: Square root of 323,761, 3 digits root, require 9 as root in the middle of calculation
Open: Square root of 164,836, 3 digits root, root contains Zero
Open: Square root of 11,943,936, 4 digits root

Half-multiplication table method (Hankuku method)
Open: Half-multiplication table method Theory
Open: Square root of 4,096, Basics
Open: Square root of 729, require root reduction in the steps.
Open: Square root of 2,401, require 9 as root in the middle of calculation
Open: Square root of 54,756, 3 digits root Basics
Open: Square root of 234,256, 3 digits root, require root reduction in the steps
Open: Square root of 323,761, 3 digits root, require 9 as root in the middle of calculation
Open: Square root of 501,264, 3 digits root, root contains Zero
Open: Square root of 1,1943,936, 4 digits root


Cube root calculation



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.

Triple-root method (Sankon method)
Open: Triple-root method Theory
Open: Cube root of 421,875, Basics
Open: Cube root of 42,875, wound up multiplying by 9 (Kakemodoshi in Japanese)
Open: Cube root of 110,592, require root reduction in the steps
Open: Cube root of 59,319, require 9 as root in the steps
Open: Cube root of 385,828,352, 3 digits root, Basics
Open: Cube root of 128,024,064, 3 digits root, root contains Zero
Open: Cube root of 45,118,016, 3 digits root, 1 digit left shift
Open: Cube root of 721,734,273, 3 digits root,require 9 as root in the steps
Open: Cube root of 5,735,339, 3 digits root,　require excessive root modification
Open: Cube root of 12,895,213,625, 4 digits root

1/3-multiplication table method (Sanbunkuku method)
Open: Cube root of 474,552, 2 digits root
Open: Cube root of 421,875, 2 digits root
Open: Cube root of 110,592, 2 digits root, require root reduction in the steps
Open: Cube root of 59,319, 2 digits root, require 9 as root in the steps
Open: Cube root of 12,812,904, 3 digits root, Basics


Other

Open: How to solve Cube root of 1729.03 using abacus? (Feynman v.s. Abacus man)
Open: How to calculate N-th root using calculator with [SQRT] key
Open: How to calculate N-th root using calculator WITHOUT [SQRT] key


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