Cube Root List 1 to 100

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What is Cube Root?

The cube root of a number a is that number which when multiplied by itself three times gives the number ‘a’ itself. The cube root is the inverse operation of cubing a number. The cube root symbols is ∛, it is the “radical” symbol (used for square roots) with a little three to mean cube root. 

If n is a perfect cube for any integer m i.e., n = m³, then m is called the cube root of n and it is denoted by m = ∛n.

Cube root list 1 to 100 will help students to solve the cube root problem easily, accurately and with speed.


Cube Root of 1 to 30

The cube root from 1 to 100 will help students to solve mathematical problems. List of cubic roots of numbers from 1 to 100 is provided here in a tabular format. The cube root has many applications in Maths, especially in geometry where we find the volume of different solid shapes, measured in cubic units. It will help us to find the dimensions of solids. For example, a cube has volume ‘x’ cubic meter, then we can find the side-length of the cube by evaluating the cube root of its volume, i.e., side = ∛x . Let us see the values of cubic roots of numbers from 1 to 100.

Cube Root List 1 to 100

Number

Cube Root (3√)

1

1.000

2

1.260

3

1.442

4

1.587

5

1.710

6

1.817

7

1.913

8

2.000

9

2.080

10

2.154

11

2.224

12

2.289

13

2.351

14

2.410

15

2.466

16

2.520

17

2.571

18

2.621

19

2.668

20

2.714

21

2.759

22

2.802

23

2.844

24

2.884

25

2.924

26

2.962

27

3.000

28

3.037

29

3.072

30

3.107

31

3.141

32

3.175

33

3.208

34

3.240

35

3.271

36

3.302

37

3.332

38

3.362

39

3.391

40

3.420

41

3.448

42

3.476

43

3.503

44

3.530

45

3.557

46

3.583

47

3.609

48

3.634

49

3.659

50

3.684

51

3.708

52

3.733

53

3.756

54

3.780

55

3.803

56

3.826

57

3.849

58

3.871

59

3.893

60

3.915

61

3.936

62

3.958

63

3.979

64

4.000

65

4.021

66

4.041

67

4.062

68

4.082

69

4.102

70

4.121

71

4.141

72

4.160

73

4.179

74

4.198

75

4.217

76

4.236

77

4.254

78

4.273

79

4.291

80

4.309

81

4.327

82

4.344

83

4.362

84

4.380

85

4.397

86

4.414

87

4.431

88

4.448

89

4.465

90

4.481

91

4.498

92

4.514

93

4.531

94

4.547

95

4.563

96

4.579

97

4.595

98

4.610

99

4.626

100

4.642


Finding the Cube Root of a Perfect Cube

Recall that a perfect cube is the number that is the result of multiplying a number with itself  3 times.

We can think of cube roots in the same context that we view square roots. When we take the square root of a perfect square, we are searching for the number, that when multiplied by itself two times, results in the perfect square. Similarly, when we are finding the cube root of the perfect cube, we are searching for the number that when multiplied by itself three times, results in the perfect cube. 

Let's solve an example.

Find ∛343

Solution: To find this, we first need to break 343 into its prime factorization. To do so, we need to find the first pair of factors that include a prime number. For  343, this first pair will be 7 and 49. 7 cannot be broken down any further, but 49 can be broken into 7and 7. Therefore, we can say that ∛343= ∛7 x 7 x 7, so we can say that the cube root of 343 is 7, where 7 x 7 x 7 = 343


Solved Examples

Example 1:  Solve ∛4 - ∛2.

Solution: From the table, we can get the value of ∛4  and ∛2 

∛4 = 1.587

∛2 = 1.260

Therefore,

∛4  + ∛2 = 1.587 + 1.260

= 0.327

Example 2: Evaluate the value of 6∛4

Solution: We know

∛4 = 1.587

Therefore,

6∛4  = 6 x 1.587

= 9.522


Quiz Time

Find the value of:

  1. Evaluate 3∛9 + 7∛4 

  2. Solve ∛9 - ∛3

FAQ (Frequently Asked Questions)

1. What is Cube and Cube Root ?

Answer: 

Definition of Cube

If a number is multiple three times with itself, then the result of this multiplication is called the cube of that number. Example: cube of 6 = 6 × 6 × 6 = 216.

Definition of Cube Root 

The cube root is that number which on cubing itself gives the given number. The cube root is denoted by the symbol ‘ ∛ ’. Example, ∛8 =∛2 × 2 × 2 = 2

2. How to calculate Cube Root of a number by Prime Factorisation Method?

Answer:

Prime Factorisation Method 

This method has the following steps

Step 1: Find the product of prime factors of the given number.

Step 2: Keep these factors in a group of three.

Step 3: Take the product of these prime factors picking one out of every group ( group of three) of the same primes. The product of these numbers gives us the cube root of a given number.

Ex. Find the cube root of 9261.

(A) 22

(B) 21

(C) 23

(D) 24

Solution

3

9261

3

3087

3

1029

7

343

7

49

7

7


1

Prime factors of 9261

= (3×3×3)×(7×7×7)

Now, taking one number from each group of three, and evaluating it we get

= 3 x 7

∛9261 = 21