6 rule of Vedic Mathematics with three
example
Answers
EKĀDHIKENA PŪRVEŅA
The Sutra (formula) 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 of 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.
NIKHILAM NAVATAS�CHARAMAM DASATAH
The formula simply means : �all from 9 and the last from 10�
The formula can be very effectively applied in multiplication of numbers, which are nearer to bases like 10, 100, 1000 i.e., to the powers of 10(eg: 96 x 98 or 102 x 104). The procedure of multiplication using the Nikhilam involves minimum number of steps, space, time saving and only mental calculation. The numbers taken can be either less or more than the base considered.
URDHVA TIRYAGBHYAM
Urdhva � tiryagbhyam is the general formula applicable to all cases of multiplication and also in the division of a large number by another large number. It means �Vertically and cross wise.�
Now let us apply this sutra to �Multiplication of two 2 digit numbers�.
Ex. Find the product 14 X 12
SOL: Steps:
i) 4 X 6 = 24 : 2, the carried over digit is placed below the second digit.
ii) (3 X 6) + (4 x 1) = 18 + 4 = 22 ; 2, the carried over digit is placed below third digit.
iii) (2 X 6) + (3 X 1) + (4 X 3) = 12 + 3 + 12 = 27 ; 2, the carried over digit is placed below fourth digit.
iv) (2 X 1) + ( 3 X 3) = 2 + 9 = 11; 1, the carried over digit is placed below fifth digit.
v) ( 2 X 3 ) = 6.
vi) Respective digits are added.
YAVADADHIKAM TAAVADAHIKIKRITYA VARGANCHA YOJAYET
This sutra means whatever the extent of its surplus, increment it still further to that very extent; and also set up the square of that surplus. This sutra is very useful in calculating the sqaures of numbers nearer(greater) to powers of 10.
For instance: in computing the square of 103 we go through the following steps:
1. The nearest power of 10 to 103 is 100.
2. Therefore, let us take 100 as our base.
3. Since 103 is 3 more than 100(base), we call 3 as the surplus.
4. Increase the given number further by an amount equal to the surplus.
i.e., perform ( 103 + 3 ) = 106. This is the left side of our answer!!.
5. On the right hand side put the square of the surplus, that is square of 3 = 09.
6. Append the results from step 4 and 5 to get the result.
Hence the answer is 10609.