Squaring of a number ending with 1 (one)

This technique works well for squaring number ending with 1. If you multiply the numbers the traditional way you will see why this works.
For example:
     31² =
Firstly, subtract 1 from the number. The number now ends in zero and will be quite easy to square now.
     30² = 900 (3 x 3 x 10 x 10)
This is our sub-total.

Secondly, add together 30 and 31 -- the number we squared plus the number we want to square.
     30 + 31 = 61
Add this to our sub-total, 900, to get 961 (900 + 61) , which becomes the answer.
Note: For the second step you can simply double the number we squared, 30 x 2 and then add 1.



Another example is:

    121²       =
    121 - 1 = 120
    120²       = 14400 (12 x 12 x 10 x 10)
    120 + 121 = 241
    14400 + 241 = 14641  [Answer]


Self Exercises :-
a) 21² =
b) 41² =
c) 81² =
d) 141² =