So, here’s just another math trick:

Suppose, we have a number like 106 and we want to square it. So,we’re taking 100 as the number we compare to and 106 = 100 + (6)

Now, we add 6 to 106. This gets us 106+6 = 112     
  
Now, we keep 112 as the leftmost three digits of the answer. 
                                                                        We square 6 and get 6*6 = 36.     
                               
36 will be the right most 2 digits of the answer.     
                      
Therefore, our answer is 11236.

Now, we’ll try the same thing with a number less than 100. Let’s take 92 for an example.

100 + (-8) = 92  So, the difference from 100 is that  of (-8). So this is the number we will play with. 


We add -8 to 92 : 92 + (-8) = 84. Now, we take these as the left most digits and then add the square of (-8) as the right more TWO digits.

Therefore, the answer is 8464                                                                          

This is applicable for numbers much greater than 110 as well. But, with a difference.

Suppose we take 111 and try to square it. We will need to add 11 to it first and we get 122.

For the next step when we square 11, we get 121. But, we can only take upto 2 right-most digits. So:

122 and 121 combined together when we can only take 2 digits from 121 gives us:

122 + 1 (from the 121 carrying over) and add the 21 to the right.  = 12321

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