Most of the time students multiply both the numbers and find the square and it takes precisely more time than the method i use.

Technique

Ekadhikena Purvena

The Sutra (formula) Ekādhikena Pūrvena means: “By one more than the previous one”.

Now we relate the sutra to the ‘squaring of numbers ending in 5’. Consider the
example 25^{2}.

Here the number is 25. We have to find out the square of the number. For the
number 25, the last digit is 5 and the ‘previous’ digit is 2. Hence, ‘one more
than the previous one’, that is, 2+1=3. The Sutra, in this context, gives the
procedure’to multiply the previous digit 2 by one more than itself, that is, by 3′.
It becomes the L.H.S (left hand side) of the result, that is, 2 X 3 = 6. The R.H.S
(right hand side) of the result is5^{2}2, that is, 25.

Thus 25^{2} = 2 X 3 / 25 = 625.

In the same way,
35^{2} = 3 X (3+1) /25 = 3 X 4/ 25 = 1225;

65^{2} = 6 X 7 / 25 = 4225;

105^{2} = 10 X 11/25 = 11025;

135^{2} = 13 X 14/25 = 18225;

Watch The video below to understand the concept clearly

Apply the formula to find the squares of the numbers 15, 45, 85, 125, 175 and verify the answers.

Comment below in case you find any problem in this technique.