Squaring Numbers Easily

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Squaring is the process of multiplying a number by itself.
42 means 4 x 4 which is 16, 72 is 49, 122 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 122 (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
22 = 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.
272 = 30 x 24 + 32 = 720 + 9 = 729
552 =  50 x 60 + 52 = 3000 + 25 = 3025
1122 = 100 x 124 + 122 = 12400 + 144 = 12544
 
You can even do a double or triple application (if your head can cope!)
1722= 200 x 144 + 282 = 28800 + 282 = 28800 + (30 x 26 + 22) = 28800 + 780 + 4 = 29584
12312 = 1000 x 1462 + 2312 = 1462000 + (200 x 262 + 312) = 1462000 + 52400 + (30 x 32 + 12)

= 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!