Squaring numbers in your head

The Trick: Say you have a number, x, that you want to square.

First, find the difference between x and the nearest multiple of 10, and call that difference d.

Then, multiply (x-d) and (x+d). This should be much easier, because one of the numbers will be a multiple of 10 (based on how we defined d). After multiplying (x-d) and (x+d), just add d2, and you have your square. 

Example: Say you want to find the square of 77. The closest multiple of 10 is 80, so d will be 80 - 77 = 3. Then 77 + 3 = 80, and 77 - 3 = 74.

Multiplying these together is pretty straightforward: 74 x 80 = 70 x 80 + 4 x 80 = 5,600 + 320 = 5920. Add in the 32 = 9, and we get 5929 as our square of 77.

Once you get the hang of this method, it's a good bit quicker and easier than trying to attack 772head on.