Squaring numbers between 30 and 70

Most of us panic if asked to square a number larger than 12 and get out a calculator right away.  It turns out that this does not have to be the case for all situations, because there are some very bright individuals out there that are coming up with "math magic" for us to use.  Those individuals fully realize how lazy the human brain could be, and that if a process takes so long, then we would not approve of it anymore.  Unfortunately, this trick is limited, but the good news is that it works perfectly and is quick and easy.

The first thing to keep in mind is that this process only works for numbers between 30 and 70.  Why you might ask.  Simply because it relies on the number 50.  So anytime you have a number in the above-mentioned range, here is what you have to do:

1) To get the first two digits, work out the difference between that number and 50, and

     a) if it's less than 50, subtract the difference from 25

     b) if it's more than 50, add the difference to 25

2) To obtain the other two digits, square that difference and remember that if it's less than 10, for example if it's 4, you write it as 04. 

3) If the square of the difference is a three digit number, the idea of carrying over applies.

So how does all that look like in an example?  For instance, to get the value of 62 squared,

1) 62 - 50 = 12 and 25 + 12 = 37

2) 12 x 12 = 144

3) since 144 is a three digit number, we have to carry the 1 over to 37: (37+1)(44)

Hence, the answer is 3844.

This trick is an amazing one, but because of its limitations, I'd rather stick with another one that applies to all numbers.