Square Root of 3600

The square root of 3600 is 60. The square root of a number with its solution is represented as √3600 = ±60. Consider 60 multiplied by 60 itself or – 60 multiplied by – 60. The product is 3600. Here 3600 is called the perfect square number and ±60 is its square root. ie 60 × 60 or – 60 × – 60 is 3600. 60 will be called the principal square root as it has the positive solution for the given number 3600. Let us find if 60 is the square root for 3600, by using the prime factorisation method, long division method and repeated subtraction method. You can find the ways of Finding Square roots.

Note the Following:

The Square root of 3600 = √3600 where √ = radical, and 3600 is the radicand.

Exponential Form of Square root of 3600 = 36001/2

Solution for √3600 = ±60

The Principal Square root = 60

Square root of 3600 is Irrational = False

What is the Square root of 3600?

The square root of 3600 is 60. In other words, the square of 60 is 3600. i.e 60 × 60 is 3600. Also – 60 × – 60 is 3600. 

√3600 = ±60

How to Find the Square root of 3600?

There are three methods to find the Square root of 3600 

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

Square root of 3600 by Prime Factorisation Method

The Square root of 3600 will be obtained only if 3600 is a perfect square number. In this method, let’s divide the number with prime numbers starting with the smallest prime number 2 and increasing the divisors as applicable. The division is continued until the remainder is 1. The prime divisors are grouped into 2 with the same numbers ( as this is a square root) and the groups are multiplied to get the square root.

The given number, 3600 will be expressed as;

2

3600

2

1800

2

900

2

450

3

225

3

75

5

25

5

5

×

1

3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

Grouping into 2 with same divisors: 

Group 1 = 2 × 2, considering only 2

Group 2 = 2 × 2, considering only 2

Group 3 = 3 × 3, considering only 3

Group 4 = 5 × 5, considering only 5

Therefore, the square root of 3600 = 2 × 2 × 3 × 5 = 60.

Square root of 3600 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 3600, grouping it as 36 and 00.

Step 2: Let us find a square number that divides 36

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 

Square root of 3600

Hence the quotient is the square root of the given number. 

Therefore the Square root of 3600 is 60.

Square root of 3600 by Repeated Subtraction Method.

For finding the square root of 3600 using the repeated subtraction method, 3600 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 3600. Let us find the result in the table below. If the process of repeated subtraction leads to a negative number, then 3600 is not a perfect square number and thus will not have a perfect square root.

For the given number 3600, steps for repeated subtraction are

Step 1

3600

1

=

3599

Step 2

3599

3

=

3596

Step 3

3596

5

=

3591

Step 4

3591

7

=

3584

Step 5

3584

9

=

3575

Step 6

3575

11

=

3564

Step 7

3564

13

=

3551

Step 8

3551

15

=

3536

Step 9

3536

17

=

3519

Step 10

3519

19

=

3500

Step 11

3500

21

=

3479

Step 12

3479

23

=

3456

Step 13

3456

25

=

3431

Step 14

3431

27

=

3404

Step 15

3404

29

=

3375

Step 16

3375

31

=

3344

Step 17

3344

33

=

3311

Step 18

3311

35

=

3276

Step 19

3276

37

=

3239

Step 20

3239

39

=

3200

Step 21

3200

41

=

3159

Step 22

3159

43

=

3116

Step 23

3116

45

=

3071

Step 24

3071

47

=

3024

Step 25

3024

49

=

2975

Step 26

2975

51

=

2924

Step 27

2924

53

=

2871

Step 28

2871

55

=

2816

Step 29

2816

57

=

2759

Step 30

2759

59

=

2700

Step 31

2700

61

=

2639

Step 32

2639

63

=

2576

Step 33

2576

65

=

2511

Step 34

2511

67

=

2444

Step 35

2444

69

=

2375

Step 36

2375

71

=

2304

Step 37

2304

73

=

2231

Step 38

2231

75

=

2156

Step 39

2156

77

=

2079

Step 40

2079

79

=

2000

Step 41

2000

81

=

1919

Step 42

1919

83

=

1836

Step 43

1836

85

=

1751

Step 44

1751

87

=

1664

Step 45

1664

89

=

1575

Step 46

1575

91

=

1484

Step 47

1484

93

=

1391

Step 48

1391

95

=

1296

Step 49

1296

97

=

1199

Step 50

1199

99

=

1100

Step 51

1100

101

=

999

Step 52

999

103

=

896

Step 53

896

105

=

791

Step 54

791

107

=

684

Step 55

684

109

=

575

Step 56

575

111

=

464

Step 57

464

113

=

351

Step 58

351

115

=

236

Step 59

236

117

=

119

Step 60

119

119

=

0

Since the result of zero is obtained in the 60th Step, the square root of 3600 is 60.

Video Lessons

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Finding Square roots

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Solved Examples

1. Which number less than 3600 is a perfect square number?

Solution: 3481 is less than 3600 which is a perfect square number. Its square root is 59.

2. What is the square of 60?

Solution: 60 square is 3600.

Frequently Asked Questions on Square root of 3600

Q1

What is the Square root of 3600?

The Square root of 3600 is 60.
Q2

3600 is a perfect square number. Why?

60 multiplied by itself gives 3600, hence 3600 is a perfect square number.
Q3

5 is one of the prime factors of 3600. True or False?

True. 5 is also a prime factor of 3600.
Q4

What is 60 square?

60 square is 3600.
Q5

60 is a perfect square number. True or False?

False. 60 is not a perfect square number.

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