Squaring is the process of multiplying a number by itself.

4^{2} means 4 x 4 which is 16, 7^{2} is 49, 12^{2} is 144. You may be familiar with the square numbers 1,4,9,16,25,36,49,64....and so on.

When we square large numbers, it can be daunting, seem impossible, without the use of a calculator.

Not anymore, here is an easy method to square larger or awkward numbers in your head.

Let's first take 12^{2} (we know is 144). We can think of this as 12 x 12

Now pretend that doing 12 x 12 is too hard in your head, do this instead:

12 x 12

Add 2 to the first, and subtract 2 from the second, 2 is the "amender"

14 x 10 = 140 (a much simpler calculation)

The 2 that we used to add and subtract from 12 should now be squared and added on

2^{2} = 4

140 + 4 = 144

Simply reduce and increase simultaneously with an "amender" number to find an easy multiplier, multiply them and add the square of the "amender"

If that seems a bit pointless for a small number like 12, try it with another number.

27^{2} = 30 x 24 + 3^{2} = 720 + 9 = 729

55^{2} = 50 x 60 + 5^{2} = 3000 + 25 = 3025

112^{2} = 100 x 124 + 12^{2} = 12400 + 144 = 12544

You can even do a double or triple application (if your head can cope!)

172^{2}= 200 x 144 + 28^{2} = 28800 + 28^{2} = 28800 + (30 x 26 + 2^{2}) = 28800 + 780 + 4 = 29584

1231^{2} = 1000 x 1462 + 231^{2} = 1462000 + (200 x 262 + 31^{2}) = 1462000 + 52400 + (30 x 32 + 1^{2})

= 1462000 + 52400 + 960 + 1 = 1515361

Ok so maybe it can get a little crazy, and a calculator might be a welcomed addition to the solution, but it's fun and requires little effort walking down the street. Try some!