Yavdumnam Taavdunikritya Vargancha Yojayet

It means whatever the extent of the deficiency ,extent it still further to that very extent and also set up the square of that deficiency .This sutra is helpful in calculating squares of numbers near (lesser) to powers of 10.

Example 1:

98^{2 =?}

Our nearest base is 100 and 98 is 2 less than 100.So '2 ' is called the deficiency.Subtract it from 98, we get 96 our left part of answer.Next,square it (02 * 02) to get the right part of answer.

98 * 98 = (98 - 2) | (2 *2)

             =  96|04

Result 98²  = 9604

Example 2:

104²=?

Our nearest base is 100 and 104 is 4 more  than 100.So '4 ' is called the surplus .Add it to 104, we get 108 our left part of answer.Next,square it (04 * 04) to get the right part of answer.

104 * 104 =(  104+4) | (4*4)

                = 108 | 16

Result 104²=10816

Example 3:

1006 ²=?
Calculating mentally as fast as we can,
(1006 +6) | 6 *6
=1012036
Result : 1006 ²=1012036

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