Finding Square of an adjacent number: One below

Likewise, you can find out square of a number that is one less than the number whose square is known.

Let me show it by taking an example:
Say you know 60² = 3600
Then 59² will be given by the following
59² = 60² - (60 + 59) = 3600 - 119 = 3481
or Say you know 25² = 625 then
24² = 625 - (25 + 24) = 576
Apply it to find square of a digit, which is one, less than the square of known digit. This works very well for the complete range of numbers.

More details can be found at Magical Methods