Mental Calculation of Subsequent number 's Square

It is practically easy to calculate the square of the subsequent number if you know the square of the number.
For example, if you know the square of 10, You can figure out the square of 11 mentally and instantaneously.
Here is how you can do it.
Continuing the above example, Square of 10 is 100, So, square of 11 will be 121.
How ???

First, we multiply 10 with 2 to get 20 and add 1 to it to get 21. [We used: 2A + 1 ( Where A is 10 here)]
Next, we add 21 to 100 (Because 100 is the square of 10)


Similarly, if we want to calculate 51², then
We, Know 50²=2500;
So, 51²= 2500 + (2 x 50) + 1
= 2500 + 100 + 1
= 2601 (Easy, isn't it ?? )

Theory behind it-
(a + b)²= a² + 2ab + b² 

If we know a²,  and b is  1 , then  , formula becomes

(a + 1)²= a² + 2a + 1

So, its very easy to solve such square in your head alone. You can do it mentally with a little practice.

Self Exercises:-

a) 61²=
b) 13²=
c) 71²=

Note: This method can also be used for numbers which are not subsequent, this can be dont by placing any other number in place of "b" in the formula.