Square Numbers – I bet you didn’t know this!
By Toby Evans Yr 8
I believe that square numbers are one of the most interesting types of numerical values. They are formed when one number is multiplied by itself, and there are interesting outcomes when they are used in mathematical problems, for example, Pythagoras’ theorem uses square numbers to solve many geometrical problems. However, there are some less known characteristics of squares, one of which I will show you in this article. You can use this to impress your friends and parents. Here is a small exercise for you to try.
Task
Pick two different whole numbers , for example 3 and 4
Square the numbers then add the squares of the numbers together , in this example we have 9 + 16 = 25
Double your answer and write this down , in this example we would write down 2 x 25= 50
Calculate the sum of the two different numbers , in this example 3+4=7
Calculate the difference between the two numbers , in this example 4-3 = 1
Square these two answers and then add the squares together , in this example we have 49 + 1 = 50
Take away from this answer the number that you have written down
What is your total?
ZERO
ZERO
ZERO
ZERO
ZERO ZERO
Try doing this for some other numbers, I tried the following pairs:
3 2 + 4 2 = 25 , 25 x 2=50 and 7 2 + 1 2 = 50, 50 – 50 = 0
4 2 + 6 2 = 52, 52 x 2=104 and 10 2 + 2 2 =104, 104 – 104 = 0
5 2 + 9 2 = 106 , 106 x 2= 212 and 14 2 + 4 2 = 212, 212 – 212 = 0
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