Vedic Mathematical tricks -1

Vedic Mathematics is the mathematical presentation of sixteen simple mathematical formulas from the Vedas. In the Artharva veda we can find a significant amount of mathematics. This formulas can be used for almost every branch of Mathematics. This can be used even to complex problems involving a large number of mathematical operations. We will see use of some of this formulas over here. 

1. Ekadhikena Purvena

The term Ekādhikena Pūrvena means: “By one more than the previous one”.

Now see the use of this formula-

Use for squaring of numbers ending in 5 :

example 35²-

 

Now relate this formula over here.

Over here the we have to find out the square of the number 35. For this number 35, the last digit is 5. So, previous digit is 3. Now formula says one more than the previous one. So, We get-

3+1=4

Now multiply this result with the previous no, we get-

3X4=12

This is first part of the answer.

 

2nd part is even easier and always be same.

I.E., square of the last digit which is always 5², that is, 25.

Thus 35² = 3 X 4 / 25 = 1225.

In the same way,

65²= 6 X 7 / 25 = 4225;

105²= 10 X 11/25 = 11025;

135²= 13 X 14/25 = 18225;

This formulas are not fluke at all. This formula can also be proved  algebraically. Consider-

(ax + b)² Ξ a². x²+  2abx + b².

say,  x = 10  and b = 5 so,

(10a + 5) ² =  a² . 10²  + 2. 10a . 5 + 5²

=    a² . 10²+ a.10²+ 5²

=    (a²+ a ) . 10² +5²

 

Example: 45 = (40 + 5)², It is of the form (ax+b)² for a = 4, x=10 and b = 5. giving the answer a (a+1) / 25

      

     Answer- 4 (4+1) / 25 + 4 X 5 / 25 = 2025

2. Nikhilam navatascaramam Dasatah

  

This term means “all from 9 and the last from 10”.

Now use this formula for multiplication for two base line numbers.

Example-1: 98 X 97

Find differences of this numbers with its base. That is 100.

So, 98  - 02

       97 - 03

         

Now multiply this differences-

02 X 03= 06 (Last part of your answer)

Now crossly find difference between any main number and difference of other main number.

So, 98-03=95 or 97-02=95

Answer= 9506

You can check this for numbers close to 1000 also. Say 997 X 992. Base is 1000.

Example-2: 996 X1008

996   - 004

1008 - 008

 Step-1: 004 X 008=032

 Step-2: 1000-032=968(Last part of the answer)

 Step-3: 996+008=1004 or 1008-004=1004

 Step-4: 1004-1=1003(First part of the answer)

Answer- 1003968.

Example-3: 104 X 108

104  - 04

108  - 08

 Step-1: 04 X 08=032(Last part of the answer)

 Step-2: 104+08=112 or 108+04=112(First part of the answer)

Answer- 11232

I will also post other tricks using this formulas very soon. I will also try to bring other formulas also. Before that please give your review about it.