Square Root of 3721

The square root of 3721 is 61. The square root of a number with its solution is represented as √3721 = ±61. When a number is multiplied by itself, the product is termed as the square number. To determine the square root of 3721, we need to identify the number x, such that x × x = 3721. Note that the value of x can be either positive or negative as it is being multiplied by itself. The product, however, will be positive only. The methods to determine the value of x are the prime factorization method, Repeated subtraction method and Long division method. All these 3 methods are detailed in the article below. You can find ways of Finding Square roots.

Note the Following:

The Square root of 3721 = √3721 where ‘√’ = radical, and 3721 is the radicand.

Exponential Form of Square root of 3721 = 37211/2

Solution for √3721 = ±61

The Principal Square root = 61

Square root of 3721 is Irrational = False

What is the Square root of 3721?

The square root of 3721 is 61. In other words, the square of 61 is 3721. i.e., 61 × 61 is 3721. Also, – 61 × – 61 is 3721. 

√3721 = ±61

How to Find the Square root of 3721?

There are three methods to find the Square root of 3721 

  • Prime Factorisation method
  • Long Division method
  • Repeated Subtraction method

Square root of 3721 by Prime Factorisation Method

The Square root of 3721 will be obtained only if 3721 is a perfect square number. In this method, let’s divide the number with prime numbers. Since 3721 has only 1, 61 and 3721 as the prime factors. Dividing 3721 with 61, and grouping 61 and removing 61 from the root forms the square root of 3721.

The given number, 3721 will be expressed as;

61

3721

61

61

×

1

3721 = 61 × 61

√3721 = √(61 × 61)

√3721 = 61

Therefore the square root of 3721 = 61.

Square root of 3721 by Long Division Method

Follow the below mentioned steps that details the long division method;

Step 1:  Grouping the given number into pairs

The given number is 3721, grouping it as 37 and 21.

Step 2: Let us find a square number that divides 37

i.e., 

4 × 4 = 16

5 × 5 = 25 

6 × 6 = 36 

The square number that is to be considered for dividing 36 will be 6 × 6 = 36

Step 3: Continue the division using the next number 21

 

Square root of 3721

The division is complete as the remainder is zero. Hence the quotient is the square root of the given number which is 61. 

Therefore the Square root of 3721 is 61.

Square root of 3721 by Repeated Subtraction Method.

For finding the square root of 3721 using the repeated subtraction method, 3721 is first subtracted by 1, the resultant by 3, the next resultant by 5 and so on. The subtraction is stopped when the resultant becomes zero. The step at which the result becomes zero, forms the square root of 3721. Let us find the result in the table below. If the process of repeated subtraction leads to a negative number, then 3721 is not a perfect square number and thus will not have a perfect square root.

For the given number 3721, steps for repeated subtraction are

Step 1

3721

1

=

3720

Step 2

3720

3

=

3717

Step 3

3717

5

=

3712

Step 4

3712

7

=

3705

Step 5

3705

9

=

3696

Step 6

3696

11

=

3685

Step 7

3685

13

=

3672

Step 8

3672

15

=

3657

Step 9

3657

17

=

3640

Step 10

3640

19

=

3621

Step 11

3621

21

=

3600

Step 12

3600

23

=

3577

Step 13

3577

25

=

3552

Step 14

3552

27

=

3525

Step 15

3525

29

=

3496

Step 16

3496

31

=

3465

Step 17

3465

33

=

3432

Step 18

3432

35

=

3397

Step 19

3397

37

=

3360

Step 20

3360

39

=

3321

Step 21

3321

41

=

3280

Step 22

3280

43

=

3237

Step 23

3237

45

=

3192

Step 24

3192

47

=

3145

Step 25

3145

49

=

3096

Step 26

3096

51

=

3045

Step 27

3045

53

=

2992

Step 28

2992

55

=

2937

Step 29

2937

57

=

2880

Step 30

2880

59

=

2821

Step 31

2821

61

=

2760

Step 32

2760

63

=

2697

Step 33

2697

65

=

2632

Step 34

2632

67

=

2565

Step 35

2565

69

=

2496

Step 36

2496

71

=

2425

Step 37

2425

73

=

2352

Step 38

2352

75

=

2277

Step 39

2277

77

=

2200

Step 40

2200

79

=

2121

Step 41

2121

81

=

2040

Step 42

2040

83

=

1957

Step 43

1957

85

=

1872

Step 44

1872

87

=

1785

Step 45

1785

89

=

1696

Step 46

1696

91

=

1605

Step 47

1605

93

=

1512

Step 48

1512

95

=

1417

Step 49

1417

97

=

1320

Step 50

1320

99

=

1221

Step 51

1221

101

=

1120

Step 52

1120

103

=

1017

Step 53

1017

105

=

912

Step 54

912

107

=

805

Step 55

805

109

=

696

Step 56

696

111

=

585

Step 57

585

113

=

472

Step 58

472

115

=

357

Step 59

357

117

=

240

Step 60

240

119

=

121

Step 61

121

121

=

0

Since the result of zero is obtained in the 61th Step, the square root of 3721 is 61.

Video Lessons

Visualising square roots

Finding Square roots

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Solved Examples

1. Which number less than 3721 is a perfect square number?

3600 is less than 3721 which is a perfect square number. Its square root is 60.

2. What is the square of 61?

61 square is 3721.

Frequently Asked Questions on Square root of 3721

Q1

What is the Square root of 3721?

The Square root of 3721 is 61.
Q2

3721 is a perfect square number. Why?

61 multiplied by itself gives 3721, hence 3721 is a perfect square number.
Q3

5 is one of the prime factors of 3721. True or False?

False. 61 is the only prime factor of 3721.
Q4

What is 61 square?

61 square is 3721.
Q5

61 is a perfect square number. True or False?

False. 61 is not a perfect square number as it is a prime number and has no other divisors.

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