YAVDUNAM TAAVDUNIKRITYA VARGANCHA YOJAYET

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

For instance in computing the square of 98 we go through the following steps:
1. The nearest power of 10 to 98 is 100.
2. Therefore, let us take 100 as our base.
3. Since 98 is 2 less than 100, we call 2 as the deficiency.
4. Decrease the given number further by an amount equal to the deficiency.
i.e., perform ( 98 -2 ) = 96. This is the left side of our answer!!.
5. On the right hand side put the square of the deficiency, that is square of 2 = 04.
6. Append the results from step 4 and 5 to get the result. Hence the answer is 9604.

Note: while calculating step 5, the number of digits in the squared number (04) should be equal to number of zeroes in the base(100). Hence in our case, the base 100 has 2 zeros and hence sqaure of 2 is 04 and not just 4.

Now consider another example: Calculate the square of 94. ( following the steps given above...)
1. The neareset power of 10 to given number 94 is 100
2. Hence the base is 100
3. Deficiency = 6
4. Subtract the deficiency from the given number ( 94 - 6 ) = 88
5. Square of deficiency = 36 ( 2 digits)
6. Append the results from step 4 and 5 to get the result. i.e., 8836

Try out calculating squares of 96, 994, 9999995