Methods of vedic maths

Methods described in the sūtras

It is not difficult to understand and apply the Vedic mathematical strategies, as long as one does not rely on the sūtras alone for mathematical insight. Those studying Vedic mathematics tend to strongly rely on the examples and explanations Tirthaji provides in his book.

All from nine and the last from ten

When subtracting from a large power of ten with many columns of zeros, it is not necessary to write the notation for "borrowing" from the column on the left. One can instead subtract the last (rightmost) digit from 10 and each other digit from 9. For example, when one is subtracting ten thousand minus 4,679, the leftmost three digits of 4,679—4, 6 and 7--are subtracted from 9, and the rightmost nonzero digit—that is, 9--is subtracted from 10, yielding the solution: 5,321. This method is also used when finding the deficit from the next larger power of ten when setting up a multiplication problem using the "cross-subtraction" method.

First corollary, when squaring numbers

"Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square (of that deficiency)"
For instance, in computing the square of 9 we go through the following steps:

1. The nearest power of 10 to 9 is 10. Therefore, let us take 10 as our base.
2. Since 9 is 1 less than 10, decrease it by the deficiency (9 - 1 = 8). This is the leftmost digit of our answer.
3. On the right hand side put the square of the deficiency, which is 1². Hence, the square of nine is 81.

Similarly, 8² = 64, 7² = 49, 6²=36.
For numbers above 10, instead of looking at the deficit we look at the surplus. For example:

and so on.

This method of squaring is based on the fact that a² = (a + b)(a − b) + b² where a is the number whose square is to be found and b is the deficit (or surplus) from nearest product of 10.

call: shubhang arora

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