How to Square 2 Digit Numbers Mentally

Squaring large numbers is not an easy task to do. However, using a right strategy and with constant practice, it can be done. Below is one method that you might want to try. This strategy only requires three steps and a lot of focus. 😉

Steps on How to Square 2 Digit Numbers Mentally

(1) Look for the difference between the number and the nearest multiple of 10. For example, we would like to square 42. The nearest multiple of 10 is 40, so the difference is 2.

(2) Multiply the following

(the number + difference) × (the numberdifference).

So, in this case, (32 + 2)(32 – 2) = 34 × 30. 

This is easier to multiply because one of them is a multiple of 10. For example, we can use the strategy for multiplication by splitting 34 into 30 and 4 and multiplying them by 30 giving us 900 + 120 = 1020

(3) Add the square of the difference to the result in (2).

The square or 2 is 4, so 1020 + 4 = 1024.

So, 322 = 1024 (Try checking if you want).

Let’s try another example. Let’s square 47.

(1) The nearest multiple of 10 is 50. So the difference of 50 and 47 is 3.

(2) Next, we multiply (47 + 3) (47 – 3) = 50(44) = 2200.

(3) Lastly, we square the difference which is 3 and add it to the result in (2) which is 2200.

2200 + 9 = 2209.

So, 472 = 2209.

This method requires practice for you to be able to master it.

Exercise:

Square the following numbers and check if your answer using the method above is correct.

  1. 48
  2. 22
  3. 59
  4. 78
  5. 92

In the next post, we are going to learn why this method works. So keep posted.

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