EKĀDHIKENA PŪRVEŅA

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

Now let us apply this 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 is 5^2, that is, 25.

Thus 25^2 = 2 X 3 / 25 = 6/25=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;

Now try to find out the squares of the numbers 15, 45, 85, 125, 175 and verify the answers.