With respect to Squares:
1. Problem: I need to know the answer of 99 multiplied by 99 (99 x 99)
Solution:
Step 1: Just add 1 to number at left and subtract 1 from number at right. This will bring it to 100 x 98 which is easily multipliable.
Step 2: Then multiply both the “1” as shown below
= (99+1)* (99-1) + (1 * 1)
= 100 * 98 + 1
= 9801
2. Solve 87 x 87
Solution:
Step 1: Add 13 to the right and subtract 13 from the left
(100 x 74)
Step 2: Then add the above to 13 x 13
100 x 74 + 13 x 13 = 7400 + 169 = 7569
Requirement: 1. We need to know thoroughly - squares from 1 to 15 ( 1 x 1, 2 x 2, ……..15 x 15) thoroughly to do these problems easily
2. In the above 2 examples, the numbers have been taken close to 100 for understanding. Other squares can be taken and multiplied upon understanding of the above concept. It can be taken in the next stage.
Disclaimer:
1. The method worked out well for me since I had interest on number crunching. It need not work for others. Heard from Vedic maths practioners that Vedic maths give much better methods for multiplying.