So, here’s another math trick and this one may be a little less intuitive to follow. It’s about squaring numbers close to 100 without that piece of machine called the calculator.
Example: Squaring 108 i.e. Calculating (108) * (108)
Now, we know that 108 differs from 100 by a +8. We make use of this and add this 8 to the number we have.
108+8 = 116
Now, we leave 116 as the left most digits of the answer and take the square of just 8. We get 8*8 = 64.
Therefore, our answer is : 11664
And voila, your calculator agrees!
Damn, I love math tricks.
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