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Vinculum Continued 

by N. S. Murty  
A New Method for ‘Finding the Cubes of Numbers’ The following method employs multiplication operations with small numbers like 1, 2, 3 and 4 to calculate the cube of any 2digit number. In the second stage, I also show how Vinculum can be used effectively to obtain the cube of any number. I provide the operational steps with explanation in a tabular form: For easy understanding I start with small numbers. Ex1. To find the cube of 12
Note: 6 is carried over to Ten’s place and 1 is carried forward to Thousands. Hence Cube of 14 is 2744. Ex.3 Find the Cube of 24 The operation is the same as with base 20 or above up to 100 except the following. Because there is no 20’s place in the decimal system, we multiply the sum of product of the number with its difference with sign with 2 when base is 20, (with 3 when the base is 30 and so on till base is 100). Any operations with respect to carry forwards will be taken up after the operation. The procedure is explained below, and the change is highlighted in bold:
For comparison and easy understanding of the procedure, I show the sequence of operations with base 40 and 30
It may be noted that using base 40 is easy since we have to manipulate with small numbers.
Take x as base and the working will be as follows: 

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14Nov2020  
More by : N. S. Murty  
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