Impress your

friends with this simple technique: First, note that

*(50 + x)*^{2} = (25 + x)100 + x^{2}. Given this

identity, the technique is almost obvious: take the difference (

*x*) between your number and 50, add 25, then tack on two

digits representing

*x*^{2}. The description is not at all clear until you see an example or two:

52^{2} = (25+2) followed by 2^{2} = 2704

59^{2} = (25+9) followed by 9^{2} = 3481

It doesn't matter if the number you're squaring is a bit under 50, either. Just subtract the difference from 25 instead of adding (of course, you're really just *adding* a negative difference):

43^{2} = (25-7) followed by 7^{2} = 1849

For numbers less than 41 or greater than 59, the "difference squared" term is longer than two digits; but if you're good enough, the same technique can be used to speed up mental squaring of these numbers also. You just have to perform an addition with carry instead of tacking the squared difference onto the end. For example, every computer nerd knows that 32 squared is 1024, so to square 82, instead of (25+32) followed by 1024, which the above procedure would dictate, just do this addition:

5700+
1024
____
6724

Of course, attempting three digit

numbers would just be silly.