Calculating the square of numbers like 8, 9, etc., is easy but calculating the square of a number like 105 without using a calculator.

There is an interesting way to calculate the square of large numbers like 255 without using a calculator. It’s probably not easy to do it in your mind but you can do it on a piece of paper. It’s essentially a way to calculate the square root of numbers that have a 5 in 1’s place value. It does not matter what sort of digits you might have in the other place values but the 1’s place value has to be a 5.

Click to see how to derive the formula

So the formula will be (x5)^2 = x(x+1)100 + 25

The formula above was derived for a 2-digit number but it can be used for any number with any number of digits provided that the number has a 5 in the 1’s place. For example, if you were to calculate 115^2, you’d simply use the formula as follows:

115^2 = 11(12)100 * 25 = 13225

You can learn how this formula was created and based on that, you can create any sort of formula for any kind of situation you might find yourself in.