Handy Math Trick : Squaring two digit, complex numbers in your head

Answer this quick without using your calculator. What's 19²? The answer is 361. Did you managed to get that correctly or did you had to cheat?

There's a simple trick you can use to square complex, two digit numbers in your head. If you knew the trick, you'd answer the above math question as fast as me too.

Arithmetic doesn't always have to be done the way you were taught in school. Let's take another example. What is 27²?

If you were to use conventional method, you'd do 27x20 + 27x7 = 540 + 189 = 729. I bet it took some while to get that solution. Am I right?

But there's a much simpler and faster way. Try this. 30x 24 + 3².Since you probably know that 30x24 is 720 and 3² is 9, you would very quickly arrive to the solution of 729. Well, want to know the trick?

The rule is that if you want to square number X, first round it up to nearest multiple of 10. Let's call it (X + r). That will be your first operand. Then, round the same amount in the opposite direction. So, your second operand would be (X - r). So, the final solution to the math problem will be :

X² = (X + r)  x (X - r) + r²

where, r is the amount you rounded. So, r² will only be either one of these values : 1, 4, 9, 16, 25.

Explanation to the trick :
This trick works because...

(X + r)  x (X - r) + r² = X² +Xr - Xr -r² +r² = X²

Now, let me test you again. What's 33²? How much time did you took this time?

If you've got any other useful math tips, I'd love to hear it in the comments.