Fun with mathematics I

I found many interesting methods to solve mathematical problems. In this blog, I'll post some of them.

How to find square of a number quickly ? 
Multiplying two numbers will be easy if one of them is a multiple of 10. There is also a high probability that a person knows the squares of small numbers by heart. If we incorporate these two ideas, we can get a quicker solution to get the square of a number.
Sample problems and Solutions [1] :
It's based on the algebra identity for the difference of squares, but with a twist!
54^2 = 50 * 58 + 4^2 = 2916.
42^2 = 40 * 44 + 2^2 = 1764.
37^2 = 34 * 40 + 3^2 = 1369.
Logic
a2 = (a-b)(a+b) + b2.

How to find square of a TWO DIGIT number that ENDS in 5? 
Here again, I've taken examples from [1]. Its very easy to calculate the square of a given two digit number if it ends in 5.
Remember three things
* Two digit number
* Ends in 5
* Find square
Sample problems and Solutions
45^2 = 2025
85^2 = 7225, etc.
Logic:
If the first digit is N and the second digit is 5, then the last 2 digits of the answer will be 25, and the preceding digits will be N*(N+1).

References:

1. Su, Francis E., et al. "Squaring Quickly." Mudd Math Fun Facts.