Calculating Square of Large Numbers

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.

Author: Gahara Raschedian

Math and Science Teacher

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