One I learned years ago is squaring numbers that end in 5 — like 25 x 25, 55 x 55 and so on.

The answer always ends in 25 and the first part in always the beginning number times itself plus one.

So 25 x 25 is 3 x 2 and then 25 or 625.

55 x 55 is 6 x 5 and then 25 or 3025.

I use this for estimating. If I want to know what 43 x 42 is, I know it’s less than 45 x 45 or 2025 and more than 40 x 40 which is 1600.

So I’d first guess 1800 but then notice that it has to end in six, so I’d guess 1806. And I’d be right in this case and darn close in many others.