Contributed by:

This PDF contains :

1. Introduction,

2. Methods,

3. Uses,

4. Conclusion

1. Introduction,

2. Methods,

3. Uses,

4. Conclusion

1.
International Journal of Research in Engineering, Science and Management 519

Volume-3, Issue-8, August-2020

journals.resaim.com/ijresm | ISSN (Online): 2581-5792 | RESAIM Publishing

Square Root by Using of Vedic Mathematics

Divykant Maheshbhai Parmar*

Assistant Teacher, Vasai Primary Boy School No.1, Vijapur, India

*Corresponding author: parmardivya44@gmail.com

Abstract: Vedic Mathematics can definitely solve mathematical The major difference between the prevailing mathematical

numerical calculations in faster way. Some Vedic Math Scholars system and the Vedic system is that, prevalent system depends

mentioned that Using Vedic Math tricks you can do calculations on formulas, whereas the Vedic system depends on logic.

10-15 times faster than our usual methods. I agree this to some

extent because some methods in Vedic Mathematics are really very What do you mean by square root?

fast. But some of this methods are dependent on the specific A number when multiplied by itself produces a specified

numbers which are to be calculated. They are called specific number.

methods. In this paper we use a method Vedic mathematics for So the problem is when a number is given, we have to

find a roots of numbers. determine which is the number which when multiplied by itself

will result in the given number.

Keywords: Vedic Mathematics, Square roots, Method, Number.

How to calculate square root by Vedic mathematics?

Before we actually explore and understand the Vedic math

1. Introduction

methods, there are certain simple but important facts, which

Vedic Mathematics is the name given to the ancient system have to be borne in mind.

of Indian Mathematics which was rediscovered from the Vedas 1. We have to look at the numbers from 1 to 10.

between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884- Squares of these numbers are

1960). According to his research all of mathematics is based 1,4,9,16,25,36,49,64,81,100

on sixteen Sutras, or word-formulae. For example, 'Vertically From this we can infer that

and Crosswise` is one of these Sutras. These formulae describe Square root of any number which ends with 1 will end with

the way the mind naturally works and are therefore a great help 1 or 9 (1 and 9 add up to 10)

in directing the student to the appropriate method of solution. Square root of any number which ends with 4 will end with

2 or 8 (2+8=10)

2. Methods Square root of any number which ends with 9 will end with

Tirthaji Maharaja has classified tricks to find square 3 or 7 (3+7=10)

roots in Vedic Mathematics in Specific and General Methods. Square root of any number which ends with 6 will end with

Specific Multiplication Methods can be applied to a Perfect 6 or 4 (6 + 4=10)

Square. While General Square Root Methods can be applied to The above stated fact is very logical and rather than

any type of number. remembering it, you have to understand the logic behind it. In

Vedic Mathematics with its roots in Atharvaveda is an Vedic mathematics, the stress is in understanding the principles

ancient Indian system of doing calculations, which is fast and rather than rote learning.

accurate. 2. In Vedic mathematics to find the square root of any

In all there are 16 sutras, meaning principles, which once number, two distinct methods can be applied.

understood can be applied in different calculations with For numbers which are perfect squares, the specific method

different interpretations. The same sutra can be utilized in is applied.

solving different calculations. For numbers, which may or may not be perfect squares, the

Hence to understand Vedic Math it is essential general method is applied.

1. To understand the sutras. Specific Method:

2. To understand the application of the sutra in various This method is suitable for numbers which are perfect square.

calculations. Let us take the number 2304.

The prerequisite is that the user should know the This number ends with 4,

mathematical table from 1 to 9. With just this basic information In the next step we have to find two squares of multiple of 10

you can go ahead and be an expert in Vedic mathematics, just between which this number lies.

by persistence and practice. So 10 x 10 = 100 and 20 x 20 = 400 but, our number 2304

In all there are sixteen sutras and 13 up sutras which is good does not lie between 100 and 400.

enough to solve any kind of quantitative problems. On the contrary 2304 lies between (40)2 and (50)2

Volume-3, Issue-8, August-2020

journals.resaim.com/ijresm | ISSN (Online): 2581-5792 | RESAIM Publishing

Square Root by Using of Vedic Mathematics

Divykant Maheshbhai Parmar*

Assistant Teacher, Vasai Primary Boy School No.1, Vijapur, India

*Corresponding author: parmardivya44@gmail.com

Abstract: Vedic Mathematics can definitely solve mathematical The major difference between the prevailing mathematical

numerical calculations in faster way. Some Vedic Math Scholars system and the Vedic system is that, prevalent system depends

mentioned that Using Vedic Math tricks you can do calculations on formulas, whereas the Vedic system depends on logic.

10-15 times faster than our usual methods. I agree this to some

extent because some methods in Vedic Mathematics are really very What do you mean by square root?

fast. But some of this methods are dependent on the specific A number when multiplied by itself produces a specified

numbers which are to be calculated. They are called specific number.

methods. In this paper we use a method Vedic mathematics for So the problem is when a number is given, we have to

find a roots of numbers. determine which is the number which when multiplied by itself

will result in the given number.

Keywords: Vedic Mathematics, Square roots, Method, Number.

How to calculate square root by Vedic mathematics?

Before we actually explore and understand the Vedic math

1. Introduction

methods, there are certain simple but important facts, which

Vedic Mathematics is the name given to the ancient system have to be borne in mind.

of Indian Mathematics which was rediscovered from the Vedas 1. We have to look at the numbers from 1 to 10.

between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884- Squares of these numbers are

1960). According to his research all of mathematics is based 1,4,9,16,25,36,49,64,81,100

on sixteen Sutras, or word-formulae. For example, 'Vertically From this we can infer that

and Crosswise` is one of these Sutras. These formulae describe Square root of any number which ends with 1 will end with

the way the mind naturally works and are therefore a great help 1 or 9 (1 and 9 add up to 10)

in directing the student to the appropriate method of solution. Square root of any number which ends with 4 will end with

2 or 8 (2+8=10)

2. Methods Square root of any number which ends with 9 will end with

Tirthaji Maharaja has classified tricks to find square 3 or 7 (3+7=10)

roots in Vedic Mathematics in Specific and General Methods. Square root of any number which ends with 6 will end with

Specific Multiplication Methods can be applied to a Perfect 6 or 4 (6 + 4=10)

Square. While General Square Root Methods can be applied to The above stated fact is very logical and rather than

any type of number. remembering it, you have to understand the logic behind it. In

Vedic Mathematics with its roots in Atharvaveda is an Vedic mathematics, the stress is in understanding the principles

ancient Indian system of doing calculations, which is fast and rather than rote learning.

accurate. 2. In Vedic mathematics to find the square root of any

In all there are 16 sutras, meaning principles, which once number, two distinct methods can be applied.

understood can be applied in different calculations with For numbers which are perfect squares, the specific method

different interpretations. The same sutra can be utilized in is applied.

solving different calculations. For numbers, which may or may not be perfect squares, the

Hence to understand Vedic Math it is essential general method is applied.

1. To understand the sutras. Specific Method:

2. To understand the application of the sutra in various This method is suitable for numbers which are perfect square.

calculations. Let us take the number 2304.

The prerequisite is that the user should know the This number ends with 4,

mathematical table from 1 to 9. With just this basic information In the next step we have to find two squares of multiple of 10

you can go ahead and be an expert in Vedic mathematics, just between which this number lies.

by persistence and practice. So 10 x 10 = 100 and 20 x 20 = 400 but, our number 2304

In all there are sixteen sutras and 13 up sutras which is good does not lie between 100 and 400.

enough to solve any kind of quantitative problems. On the contrary 2304 lies between (40)2 and (50)2

2.
International Journal of Research in Engineering, Science and Management 520

Volume-3, Issue-8, August-2020

journals.resaim.com/ijresm | ISSN (Online): 2581-5792 | RESAIM Publishing

i.e. between 1600 and 2500. And it is also closer to 50. Now from Step 2, possibilities are 43 or 47 out of

Now since the number 2304 ends with 4 we understand the which 47 is closer to 50

square root should end with either 2 or 8. 4. Hence square root = 47.

The square root lies between 40 and 50 and should end with

either 2 or 8. General Method:

With this understanding we can conclude that the square root This method is a more general method, which can be used to

could be either 42 or 48. find the square root of any number irrespective of the fact,

But we already saw that it should be closer to 50, hence the whether it is a perfect square or not.

square root of 2304 is 48. Like in the earlier method, before we go into understanding

As explained earlier, the working of vedic mathematics is this method, there is one more small technique that needs to be

more focused and based on logical thinking rather than putting understood. That technique is known as “Dwanda.”

variables into formulas and finding results. The calculation of Dwanda will depend on the number of

Let us find another number to find square root. digits of the number. That is whether it is single digit, two digit,

Let us take the number 2704. three digit, four digit and so.

2704 definitely lies between 2500 = (50)2 and 3600= (60)2 Dwanda is represented by D,

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

Since the given number is 2704 and it ends with 4, the square D(6) = 6 x 6 = 36

root should end in 2 or 8. (refer to the notes above). D(24) = 2 x 2 x 4 = 16

Analysing point no 2 and point no 3 above, we can conclude D(345) = (2x3x5) + (4x4) = 38

that the square root could be 52 or 58. D(2356) = (2x2x6) + (2x3x5) =54

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

Hence the square root should also be closer to 50 rather than We shall now generalise the Dwanda formulas,

60. D(a) = a a

Analyzing the point 4 and point 6 above, we can safely arrive D(ab) = 2 x a x b

at the conclusion that the square root of 2704 is 52. D(abc) (2 x a x c) + (b x b)

Facts for Square Roots Math tricks: D(abcd) = (2 x a x d) + (2 x b x c)

Squares of numbers from 1 to 9 are 1, 4, 9, 16, 25, 36, Please practice this Dwanda formula with some numbers

49, 64, 81, and 100. before you go further.

Square of a number cannot end with 2, 3, 7, and 8. OR Let us now look at the using the general method to find:

number ending with 2, 3, 7 and 8 cannot have perfect √12544

square root. 1.first divide the number into sets of 2,

Square root of a number ending with 1 (1, 81) ends So we get,

with either 1 or 9 (10’s compliment of each other). 1 25 44

Square root of a number ending with 4 (4, 64) ends The above table will get formed if we apply DSD Dwanda

with either 2 or 8 (10’s compliment of each other). Subtraction from above number and division.

Square root of a number ending with 9 (9, 49) ends So the digits of the answer turns out to be 1 12 00

with either 3 or 7 (10’s compliment of each other).

Square root of a number ending with 6 (16, 36) ends Where would the decimal point come?

with either 4 or 6 (10’s compliment of each other). Look at the basic number 12544…..since it has odd number

of digits we use the formula

If number is of ‘n’ digits then square root will be ‘n/2’

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

OR ‘(n+1)/2’ digits.

Based on the facts, square root method can be calculated as 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.

This shortcut method of Square Roots can be applied

The method for perfect square is relatively easier to

whenever number is perfect square.

understand and use.

Example:

Remember the following:

Square root of 2209

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

1. Number ends with 9, Since it’s a perfect square, square

9

root will end with 3 or 7.

2. You should be able to easily calculate the square of

2. Need to find 2 perfect squares (In Multiplies of 10)

multiples of 10s, i.e. 10 square, 20 square, 30 square

between which 2209 exists.

and so on.

Numbers are 1600=(402) and 2500=(502).

3. You should remember, depending on the last digit of

3. Find to whom 2209 is closer. 2209 is closer to 2500.

the given number, how to arrive at the last digit of the

Therefore square root is nearer to 50.

Volume-3, Issue-8, August-2020

journals.resaim.com/ijresm | ISSN (Online): 2581-5792 | RESAIM Publishing

i.e. between 1600 and 2500. And it is also closer to 50. Now from Step 2, possibilities are 43 or 47 out of

Now since the number 2304 ends with 4 we understand the which 47 is closer to 50

square root should end with either 2 or 8. 4. Hence square root = 47.

The square root lies between 40 and 50 and should end with

either 2 or 8. General Method:

With this understanding we can conclude that the square root This method is a more general method, which can be used to

could be either 42 or 48. find the square root of any number irrespective of the fact,

But we already saw that it should be closer to 50, hence the whether it is a perfect square or not.

square root of 2304 is 48. Like in the earlier method, before we go into understanding

As explained earlier, the working of vedic mathematics is this method, there is one more small technique that needs to be

more focused and based on logical thinking rather than putting understood. That technique is known as “Dwanda.”

variables into formulas and finding results. The calculation of Dwanda will depend on the number of

Let us find another number to find square root. digits of the number. That is whether it is single digit, two digit,

Let us take the number 2704. three digit, four digit and so.

2704 definitely lies between 2500 = (50)2 and 3600= (60)2 Dwanda is represented by D,

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

Since the given number is 2704 and it ends with 4, the square D(6) = 6 x 6 = 36

root should end in 2 or 8. (refer to the notes above). D(24) = 2 x 2 x 4 = 16

Analysing point no 2 and point no 3 above, we can conclude D(345) = (2x3x5) + (4x4) = 38

that the square root could be 52 or 58. D(2356) = (2x2x6) + (2x3x5) =54

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

Hence the square root should also be closer to 50 rather than We shall now generalise the Dwanda formulas,

60. D(a) = a a

Analyzing the point 4 and point 6 above, we can safely arrive D(ab) = 2 x a x b

at the conclusion that the square root of 2704 is 52. D(abc) (2 x a x c) + (b x b)

Facts for Square Roots Math tricks: D(abcd) = (2 x a x d) + (2 x b x c)

Squares of numbers from 1 to 9 are 1, 4, 9, 16, 25, 36, Please practice this Dwanda formula with some numbers

49, 64, 81, and 100. before you go further.

Square of a number cannot end with 2, 3, 7, and 8. OR Let us now look at the using the general method to find:

number ending with 2, 3, 7 and 8 cannot have perfect √12544

square root. 1.first divide the number into sets of 2,

Square root of a number ending with 1 (1, 81) ends So we get,

with either 1 or 9 (10’s compliment of each other). 1 25 44

Square root of a number ending with 4 (4, 64) ends The above table will get formed if we apply DSD Dwanda

with either 2 or 8 (10’s compliment of each other). Subtraction from above number and division.

Square root of a number ending with 9 (9, 49) ends So the digits of the answer turns out to be 1 12 00

with either 3 or 7 (10’s compliment of each other).

Square root of a number ending with 6 (16, 36) ends Where would the decimal point come?

with either 4 or 6 (10’s compliment of each other). Look at the basic number 12544…..since it has odd number

of digits we use the formula

If number is of ‘n’ digits then square root will be ‘n/2’

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

OR ‘(n+1)/2’ digits.

Based on the facts, square root method can be calculated as 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.

This shortcut method of Square Roots can be applied

The method for perfect square is relatively easier to

whenever number is perfect square.

understand and use.

Example:

Remember the following:

Square root of 2209

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

1. Number ends with 9, Since it’s a perfect square, square

9

root will end with 3 or 7.

2. You should be able to easily calculate the square of

2. Need to find 2 perfect squares (In Multiplies of 10)

multiples of 10s, i.e. 10 square, 20 square, 30 square

between which 2209 exists.

and so on.

Numbers are 1600=(402) and 2500=(502).

3. You should remember, depending on the last digit of

3. Find to whom 2209 is closer. 2209 is closer to 2500.

the given number, how to arrive at the last digit of the

Therefore square root is nearer to 50.

3.
International Journal of Research in Engineering, Science and Management 521

Volume-3, Issue-8, August-2020

journals.resaim.com/ijresm | ISSN (Online): 2581-5792 | RESAIM Publishing

answer. aptitude section of the competitive exam.

4. Use logical decisions, rather than formula to arrive at No need to remember any formula and dependency on

the right answer. the calculator will become almost zero.

By applying the concept of Vedic mathematics, one

3. Uses problem has many solutions.

Advantages of Using Vedic Math Tricks Most of the Vedic Mathematics Tricks apply to many

Easy Way to Learn. Vedic Math is a simpler and types of problem.

interesting way of learning the Math tricks than the It makes you creative to find the most efficient or fast

usual Math. Tricks to solve your problem Quick. It encourages the

Helps in Cross-Checking. student to see his unique way to solve the problem.

Enhance Logical Thinking. Vedic Mathematics helps to Develop the Intuition

Improve Confidence. ability of the student.

More Systematic Way of Learning. Through the concept of digital roots, everybody can

Improves the performance in Competitive Level Exams. check the validity of answer to the question.

Benefits of Vedic Math is beneficial for both who likes and A most cumbersome problem like Square, cube,

dislikes the calculation. It makes the learning of mathematics Square root or Cubic root of the larger number can be

extremely easy and fast. solved through mentally if you know Vedic

The most existing Benefits of Vedic Maths is its mathematics.

simplicity and integration of rule which is some time

looks like magic to the student, and its create interest 4. Conclusion

in student to learn math. This paper presented an overview on square root by using of

The many tedious or cumbersome problem can be Vedic mathematics.

solved through the Vedic mathematics in mind, so

don’t need to write too much. References

The Very Most Benefits of Vedic Math is It gives You [1] https://ziyyara.in/blog/easy-learn-vedic-mathematics-square-root-tips-

the 10-15 times faster result as compared to the trick.html

[2] http://mathlearners.com/vedic-mathematics/square-roots/

Western way of calculation. [3] https://vedicmathschool.org/benefits-of-vedic-maths/

Vedic Mathematics Tricks is very useful in the

Volume-3, Issue-8, August-2020

journals.resaim.com/ijresm | ISSN (Online): 2581-5792 | RESAIM Publishing

answer. aptitude section of the competitive exam.

4. Use logical decisions, rather than formula to arrive at No need to remember any formula and dependency on

the right answer. the calculator will become almost zero.

By applying the concept of Vedic mathematics, one

3. Uses problem has many solutions.

Advantages of Using Vedic Math Tricks Most of the Vedic Mathematics Tricks apply to many

Easy Way to Learn. Vedic Math is a simpler and types of problem.

interesting way of learning the Math tricks than the It makes you creative to find the most efficient or fast

usual Math. Tricks to solve your problem Quick. It encourages the

Helps in Cross-Checking. student to see his unique way to solve the problem.

Enhance Logical Thinking. Vedic Mathematics helps to Develop the Intuition

Improve Confidence. ability of the student.

More Systematic Way of Learning. Through the concept of digital roots, everybody can

Improves the performance in Competitive Level Exams. check the validity of answer to the question.

Benefits of Vedic Math is beneficial for both who likes and A most cumbersome problem like Square, cube,

dislikes the calculation. It makes the learning of mathematics Square root or Cubic root of the larger number can be

extremely easy and fast. solved through mentally if you know Vedic

The most existing Benefits of Vedic Maths is its mathematics.

simplicity and integration of rule which is some time

looks like magic to the student, and its create interest 4. Conclusion

in student to learn math. This paper presented an overview on square root by using of

The many tedious or cumbersome problem can be Vedic mathematics.

solved through the Vedic mathematics in mind, so

don’t need to write too much. References

The Very Most Benefits of Vedic Math is It gives You [1] https://ziyyara.in/blog/easy-learn-vedic-mathematics-square-root-tips-

the 10-15 times faster result as compared to the trick.html

[2] http://mathlearners.com/vedic-mathematics/square-roots/

Western way of calculation. [3] https://vedicmathschool.org/benefits-of-vedic-maths/

Vedic Mathematics Tricks is very useful in the