sutra 1 of vedic maths

EKĀDHIKENA PŪRVEŅA

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

i) Squares of numbers ending in 5 :

Now we relate the sutra to the ‘squaring of numbers ending in 5’. Consider the example 25².

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 5², that is, 25.

Thus 25² = 2 X 3 / 25 = 625.

In the same way,

35²= 3 X (3+1) /25 = 3 X 4/ 25 = 1225;

65²= 6 X 7 / 25 = 4225;

105²= 10 X 11/25 = 11025;

135²= 13 X 14/25 = 18225;