This is a neat arithmetic trick to keep in your back pocket. I learned it back in high school and it stayed with me. It goes as follows:

Let's say you want to square a number that ends in 5. Separate the 5 from the remaining digits in the number. Let $$n$$ represent the number formed by those digits. For example, if the number you want to square is 35, the number $$n$$ is 3. Now, to get your answer, simply multiply $$n$$ with $$(n+1)$$, write down the result, and insert "25" at the end. Yes, it's that simple. In our example, $$n=3$$, so $$n(n+1) = 3 \times 4 = 12$$. Thus, the square of 35 is 1225. I have shown the "12" and the "25" in two different colors, just to emphasize that we got the 12 from computing $$n(n+1)$$ and the "25" always comes for free at the end.

Let's do a bit of algebra to see why this trick works. I'll demonstrate it for two digit numbers to keep it simple. Any two digit number that ends in 5 can be written as $$10n+5$$, where $$n$$ is the first digit. Let's compute the square of this number - 

$$(10n+5)^2 = (10n+5)(10n+5)$$

$$ = 100n^2 + 100n + 25$$

$$ = 100\underline{n(n+1)} + 25$$

This means that the square must have "25" as it's bottom two digits and $$n(n+1)$$ as it's upper digits (at the hundreds place value, and higher). Trick demystified!

I hope you will keep this little trick handy and use it when you don't feel like punching numbers into a calculator or computer. You can convince yourself that the "trick" works not just for two digit numbers, but for any number that ends in 5.