square big #'s

Is there a fast way for squaring numbers that are really big … of more than three digits? Let’s pick this number: 1,002 squared. I chose 1,002 arbitrarily because I like to work with smallish big numbers, but the following formula works for any number.

(a ± b)² = a² ± 2ab + b²

a = 1000 (because 1000 is easy to work with) and b = 2

Using the formula, (1000 + 2)² = 1,000,000 + 4,000 + 4 = 1,004,004

When multiplying multiples of 10, just count the zeros. One thousand is a multiple of 10. So, with 1000 x 1000, or 1,000 squared, count the six zeros, and the answer is one million.