quick squaring of numbers

I was lying awake last night, and a little math trick came to me.

Let’s say you want to know what 256*256 is. Normally, you might need to find a calculator or pen (or if you’re a geek, you already know the answer).

The steps you would usually follow to multiply this are:

  • 256*200=51200 (easy)
  • 256*50=12800 (easy)
  • 256*6=1536 (need memory)
  • 51200+12800+1536=65536 (need memory)

relatively easy, but you need to be able to remember some things.

An easier method might be:

  • 255*255=(25*26)+”25″=(625+25)+”25″=65025
  • (255*255)+(256*2-1)=65025+511=65536

So what did I just do? I just broke the problem down to take advantage of two math tricks.

The first is very simple – any number which has a 5 at the end, squared, is equal to the number without the five multiplied by itself+1, and “25” added to the end. For instance, in the above we have (25*26), which is equal to (25*25 +25). 25*25, using he trick, is equal to (2*3)+”25″, or 625, making 25*26=625+25=650. Easy!

the second has to do with how the result of every squared number ‘n’ is n*2-1 above the result for the square of n-1. For instance, if you know that 100 squared is 10,000, you can know immediately that 101 squared is 10,000+(101*2-1)=10201.

Little tricks, but they can be surprising to people that don’t know them.

You can also do the opposite – 99 squared is 100^2-(100*2-1)=9801.


  1. I reckon you’d enjoy O’Reilly’s book “Mind Performance Hacks” by Ron Hale-Evans.
    It has a lot of tips,similar to yours, in it’s maths section.

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