I just stumbled upon this nice little trick which helps you to square numbers which are close to 100.

Let's say, you want to calculate 105*105. Then you can simply add the difference between 100 and 105 which is 5 to the 105 and get 110 which are the first three digits. Then just add 5 squared and you will get 11025 which is the result. This works for all numbers up to 150 but is more useful if the number is close to 100. By the way, it also works for numbers smaller then 100 but in that case you simply have to subtract the difference to 100 from your number.

The following video is giving you some more examples and also shows what happens for larger distances:

Neat!