Multiplication Using Nikhilam-sutra And Urdhvatiryagbhyam Sutra

By Author: Arun Kumar
Total Articles: 2
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In the first two digits of Vedic mathematics, we learned how easily we can multiply large digits. We also saw a list of Theorems with the help of which we will be able to do even the biggest calculations in seconds. Veda is the ocean of knowledge and Vedic mathematics is a drop of this ocean. Efforts will be made to know the sixteen sutras of Vedic mathematics.

Today, some shortcuts of Multiplication have come from a single drop of this bottomless ocean. With the help of Nikhilansutra and Uphyatirgabham, we will understand Shortcuts.

Some tips from Nikhilansutram:

Suppose you have to draw a square of 7:

Since 10 for 7 will be considered as base, so 7 out of 10 will be reduced as much as 7 .. It will be understood by example.

(7 - 3) / (3 * 3) = 4/9 = 49
6 2 = (6-4) / (4 * 4) = 2/16 = (2 + 1) / 6 = 36
8 2 = (8-2) / (2 * 2) = 6/4 = 64

12 2 = (12 + 2) / (2 * 2) = 14/4 = 144
14 2 = (14 + 4) / (4 * 4) = 18/16 = (18 + 1) / 6 = 196

In all these examples, because 10 is assumed to be the base, the right digit of "/" will come only and the digit in the right ...
... number which is of ten place i.e. 10th place is added to the left number.

19 2 = (19 + 9) / (9 * 9) = 28/81 = (28 + 8) / 1 = 361

Next let us know how Square is taken out of any number ending at 5 with the help of Ekadiken Puravane:
All that has to be done is that the digits after "/" will always be 25 and for the preceding digit, one has to multiply the same number by adding one to the number before 5.
1 to 15 for 2 and 65 to 6 to 7.

15 2 = (1 * 2) / 25 = 225
25 2 = (2 * 3) / 25 = 625
35 2 = (3 * 4) / 25 = 1225
75 2 = (7 * 8) / 25 = 5625

135 2 = (13 * 14) / 25 = 182/25 = 18225
195 2 = (19 * 20) / 25 = 38025

Similarly, we can also multiply those numbers whose sum of the last digits is 10 and the first digit is equal. like:

27 * 23 | It has 7 + 3 = 10 and the first digit is 2 only. That's why:
(2 * 3) / (7 * 3) = 6/21 = 621

96 * 94 = (9 * 10) / (6 * 4) = 90/24 = 9024
98 * 92 = (9 * 10) / (8 * 2) = 9016
87 * 83 = (8 * 9) / (7 * 3) = 72/21 = 7221
114 * 116 = (11 * 12) / (4 * 6) = 132/24

Vertical thread

Multiply both digits of 10th place, (Top-Left * Right-Bottom) + (Bottom-Left * Top-Right) and multiply the last digits of both numbers and write something like this:

12
11
_________
1: 1 + 2: 2 = 1: 3: 2 = 132

21
14
____________
2: 8 + 1: 4 = 2: 9: 4 = 294

37
33
___________________

9: 9 + 21: 21 = 9: 30: 21
Here we have to add the 10th place digit of the middle number to the first number and likewise add the digit of the rightmost number to the middle one.
9: 30: 21 = 9 + 3: 0 + 2: 1 = 1221

73
76
___________________
49: 42 + 21: 18 = 49: 63: 18 = 56: 4: 8 = 5548

Solution to Multiplication of Large Number in just few seconds !!!

Algebraic Equation Behind It:
(ax 2 + bx + c) by (dx 2 + ex + f)

= adx 4 + (ae + bd) x 3 + (af + be + cd) x 2 + (bf + ce) x + cf for x = 10

109
111
_____________________________________
1: 1: 10: 9: 9 = 1: 2: 0: 9: 9 = 12099

582
231
___________________________________
10: 15 + 16: 5 + 24 + 4: 8 + 6: 2
= 10: 31: 33: 14: 2 = 13: 4: 4: 4: 2 = 134442

785
362
__________________________________________
21: 42 + 24: 14 + 48 + 15: 16 + 30: 10
= 21: 66: 77: 46: 10 = 28: 4: 1: 7: 0 = 284170

In the next digit, we will know how to find the area of a large rectangle. Sq. ft and Sq. inches will be calculated without calculator :-)
And we will know how division can be done by Nikhilam Sutra.

Vedic mathematics>/a>

Vedic mathematics>/a>