In part I, I showed you how to square a three-digit number in your head by squaring the first digit, adding double the cross-product (the first digit times by the other two digits) and adding the square of the final digits, with appropriate shifting.

Now, what about something like 7982? You could, of course, work out the numbers as 49, 7 × 98 × 2 = 1372, and 9604, adding them with shifts to get 6272, then 636804 (phew!), or you could split it up differently. You could do it as (800−2)2.

That’s much easier, and it works the same way. Let me walk you through it:

  • 82=64
  • 8×−2×2=−32; shifting it and adding on, I get 6368.
  • (−2)2=04, making 636804

(Note that I write that last bit as 04 - because I’m mentally moving each sum two places to the left, I don’t want to miss out the 0 in the answer!)

The advantages of this way over the way in part 1 is that you only need to know your squares up to 50, which is much less to learn. The taking away needs a bit of practice, but it’s not all that bad.

But wait, there’s more! Next week, I’ll show you how to make your workload even less by using half-hundreds.