## Thursday, 6 October 2011

### Squaring Numbers Under 100

First, I must state that although you do not necessarily require any prior knowledge other than to be competent at maths, it does not hurt if you know the square numbers up to 10 and are reasonably good at quadratic equations.

I recently discovered this technique of timesing numbers together recently and I was pretty proud of myself and have been using to bamboozle my friends and family. However I did not create this technique, I do not know who did, but if you do please leave a comment.

I am starting by squaring a number, as the skills learnt from that will help you when you times two different numbers together, which I will cover in a later blog post.

To begin with when squaring a number we need to choose one number as a base, we will call it 'a', for example if we had 43 our base would be 40. If we had 47 however I would personally choose 50, as dealing with 3 is easier than dealing with 7. This second number we will call, 'n', to get 'n' you take the base from the original number, 'o'.

n = o-a

You may see where we are going here, we will take the equation (a+n) and square it, that is all we have to do. The product of this will be a²+2an+n². So for example if we wanted to find the answer to 76²:

a = 80, n = 76-80 = -4
80²+2(80*-4)+(-4)²
6400-640+16 = 5776

After a little bit of practice you can do this very efficiently and very quickly in your head.