Vedic Mathematics with its roots in Atharvaveda is an ancient Indian system of doing calculations, which is fast and accurate.

Swami Teerthaji Maharaj of puri, rediscovered this ancient skill and presented it to the world in the form of sutras.

In all there are 16 sutras, meaning principles, which once understood can be applied in different calculations with different interpretations. The same sutra can be utilised in solving different calculations.

Hence to understand vedic Maths, it is essential :

1. To understand the sutras.

2. To understand the application of the sutra in various calculations.

Being a different methodology, it may take some time to understand, but with some practice, very easily anyone can master the techniques and apply it successfully.

The prerequisite is that the user should know the mathematical table from 1 to 9. With just this basic information, you can go ahead and be an expert in vedic mathematics, just by persistence and practice.

Vedic math finds application in all branches , like basic arithmetic, calculus, integration, derivation, geometry, algebra and so on.

In all there are sixteen sutras and 13 upsutras which is good enough to solve any kind of quantitative problems.

To understand all the sutras, is beyond the scope of this article now. For the time being , we shall concentrate on understanding and learning the vedic maths tips and tricks to find square roots.

The major difference between the prevailing mathematical system and the vedic system is that, prevalent system depends on formulas, whereas the Vedic system depends on logic.

**What do you mean by square root?**

A number when multiplied by itself produces a specified number.

So the problem is when a number is given, we have to determine which is the number which when multiplied by itself will result in the given number.

**How to calculate square root by Vedic mathematics?**

Before we actually explore and understand the Vedic maths methods, there are certain simple but important facts, which have to be borne in mind.

1. We have to look at the numbers from 1 to 9.

Square of 1 (1^2)= 1

Square of 2 (2^2)= 4

Square of 3 (3^2)= 9

Square of 4 (4^2)=16

Square of 5 (5^2)= 25

Square of 6 (6^2)= 36

Square of 7 (7^2)= 49

Square of 8 (8^2)= 64

Square of 9 (9^2)=81

2. From this we can infer that

Square root of any number which ends with 1 will end with 1 or 9 ( 1 and 9 add up to 10)

Square root of any number which ends with 4 will end with 2 or 8 (2+8 =10)

Square root of any number which ends with 9 will end with with 3 or 7 (3+7=10)

Square root of any number which ends with 6 will end with 6 or 4 (6 + 4=10)

The above stated fact is very logical and rather than remembering it, you have to understand the logic behind it. In vedic mathematics,the stress is in understanding the principles rather than rote learning.

3. In vedic mathematics to find the square root of any number, two distinct methods can be applied.

For numbers which are perfect squares, the specific method is applied

For numbers, which may or may not be perfect squares, the general method is applied.

**Specific Method**

This method is suitable for numbers which are perfect square.

Let us take the number 2304.

This number ends with

In the next step we have to find two squares of multiple of 10 between which this number lies.

So 10 x 10 = 100 and

20 x 20 = 400 but, our number 2304 does not lie between 100 and 400.

On the contrary 2304 lies between (40)2 and (50)2.i.e between 1600 and 2500.

And it is also closer to 50 .

Now since the number 2304 ends with 4 we understand the the square root should end with either 2 or 8.

The square root lies between 40 and 50 and should end with either 2 or 8.

With this understanding we can conclude that the square root could be either 42 or 48.

But we already saw that it should be closer to 50, hence the square root of 2304 is 48.

As explained earlier, the working of vedic mathematics is more focussed and based on logical
thinking rather than putting variables into formulas and finding results.

Let us find another number to find square root.

Let us take the number 2704.

2704 definitely lies between 2500 (50)2 and 3600 (60)2 .

So obviously the square root will lie between 50 and 60.

Since the given number is 2704 and it ends with 4, the square root should end in 2 or 8. (refer to the notes above).

Analysing point no 2 and point no 3 above, we can conclude that the square root could be 52 or 58.

The given number 2704 is closer to 2500 rather than 3600.

Hence the square root should also be closer to 50 rather than 60.

Analyzing the point 4 and point 6 above, we can safely arrive at the conclusion that the square root of 2704 is 52.

**General Method**

This method is a more general method, which can be used to find the square root of any number irrespective of the fact, whether it is a perfect square or not.

Like in the earlier method, before we go into understanding this method, there is one more small technique that needs to be understood. That technique is known as “Dwanda.”

The calculation of Dwanda will depend on the number of digits of the number. That is whether it is single digit, two digit, three digit, four digit and so.

Dwanda is represented by D

So

D(6) = 6 x 6 = 36

D(24) = 2 x 2 x 4 = 16

D (345) = (2x3x5) + (4x4) = 38

D ( 2356) = (2x2x6) + (2x3x5) =54

We shall now generalise the Dwanda formulas

D(a) = a x a

D(ab) = 2 x a x b

D(abc) (2 x a x c) + (b xb)

D(abcd) = (2 x a x d) + ( 2 x b x c)

Please practice this dwanda formula with some numbers before you go further.

Let us now look at the using the general method to find :

**√12544**

1.first divide the number into sets of 2

So we get

1 25 44

The above table will get formed if we apply DSD ie.

Dwanda

Subtraction from above number

And division.

So the digits of the answer turns out to be

1 12 00

**Where would the decimal point come?**

Look at the basic number 12544…..since it has odd number of digits we use the formula

Number of digits in square root = (n+ 1)/2
= (5+1)/2 =3

So the final square root answer would be 112.00 or just 112.

Till now we have seen two ways of finding square roots. One was for perfect squares and the other for any number.

The method for perfect square is relatively easier to understand and use.

**Remember the following:**

1. You should know the squares of all numbers from 1 to 9

2. You should be able to easily calculate the square of multiples of 10s, ie. 10 square, 20 square, 30 square and so on.

3. You should remember, depending on the last digit of the given number , how to arrive at the last digit of the answer.

4. Use logical decisions, rather than formula to arrive at the right answer.