Fun Learning Way to Square a Number

There are several ways to perform multiplications. You can use a pen and paper, use a calculator, or memorize the results of particular numbers. Off course, trying to memorize the results of multiplications is not practical. You can only memorize so many. However, memorizing the multiplication table up to 10 or 12 might be a good idea to facilitate learning advanced multiplications. If you are able to memorize even up to 99, more power to you. But beyond that, I think is a waste of time and energy and takes the fun learning concept out of the equation. What a person needs to do instead is memorize and practice a method that will allow him/her to instantly process numbers in their brain to come up with the answer. I’m sure there are several methods that can practice with numbers. In this post, I will discuss only one fun and easy learning method that can be easily applied to a variety of two digit numbers.

If you know the basic multiplication table, you will be able to instantaneously answer the results of 10 × 10. 20 × 20. 30 × 30. and so on. I’m sure this should not be a problem for you. If so, here are the answers:

10 × 10 = 100. Basically this is the result of 1 × 1, and just adding the number of zeroes to the result 2 in this case. I hope I’m not insulting your intelligence or confusing you here.

20 × 20 = 400

30 × 30 = 900

If you can instantaneously know the answer for 8 × 8, for instance, which is 64, you would know

that 80 × 80 is equal to 6400.

How many seconds does it take you to do that? I hope it’s no more than 3 seconds.

Now we will only deal with multiplying like numbers—the square of a 2 digit number—so that the concept is easily understood, and then we can move on to other numbers. Let’s start with a different numbers than the, fun and easy one’s, that end with zero. How about (19²), (29²) and (39²), how can we multiply these numbers in our mind without using a pen and paper or calculator?

To do so, what we’re going to do is round them to the nearest number ending with a zero and take it from there. 

Let’s try the first number 19. The nearest zero number to it is 20. Why? Because 19 is actually (20 – 1). In other words, 19² is the same (20 – 1 )².  Realizing this much, we will first know that the answer will be close to 400, but not quite.

So the product of 19 × 19  is actually (400  - 19 – 20) = 361. 

And 29² is actually 30 × 30 = 900 – (30 – 29) = 900 – 59 = 841

The last one is 39² = (40)² - (40 – 39) = 1600 – 79 = 1521

If you didn't quite understand the concept here, don't worry, you'll get it later. In the next post, we will do similar multiplications utilizing a different approach, the Square of a Binomial. This approach should make things much easier than the previous method.

(a ± b)² = a² ± 2ab + b².