Squaring Numbers Close to 100

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.

Squaring Numbers Ending With 5

Here’s a really easy way to calculate the squares of numbers ending with a 5… suppose we are taking the square of 85:

85 * 85 = 7225

Now, the easiest way of doing this is by taking the part of the number without the last “5″ in it.. which in this example would be simply 8. Now, multiply 8 by the next number, which is 9. We get a 72… just add a 25 at the end of it and you get the answer: 7225

Therefore, as a general equation we have:

105 * 105 = (10 * 11) with a 25 at the end = 11025