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2 <p>Last updated on<strong>September 26, 2025</strong></p>

3 <p>A cube root is a value that, upon multiplied by itself thrice, gives the product known as its cube. This article explores the cube roots of numbers ranging from 1 to 30.</p>

4 <h2>Cube Root from 1 to 30</h2>

5 <p>Not all<a>numbers</a>between 1 and 30 are<a>perfect cubes</a>, so their cube roots are irrational and are generally expressed as<a>decimals</a>. There are three perfect cubes between 1 to 30. These numbers are 1, 8, and 27, and their cube roots are<a>whole numbers</a>1, 2, and 3, respectively. </p>

6 <h2>Cube Root from 1 to 30 chart</h2>

7 <p>The<a>cube</a>root chart works as an educational aid for students. It consists of all the cube roots of numbers between 1 to 30; it helps solve problems more quickly.</p>

8 <h2>List of Cube Roots from 1 to 30</h2>

9 <p>Cube roots from 1 to 30 are useful in problem-solving for number operations. Memorizing these roots helps students gain efficiency in solving<a>questions</a>. Below is a list of all cube roots between 1 and 30.</p>

10 <p><strong>Cube roots from 1 to 10</strong></p>

11 <p>The cube roots between 1 and 10, including whole numbers as well as decimals, are given below:</p>

12 <strong>Number</strong><strong>Cube Root</strong>1 1 2 1.2 3 1.44 4 1.59 5 1.71 6 1.82 7 1.91 8 2 9 2.08 10 2.15<p><strong>Cube roots from 11 to 20</strong></p>

13 <p>As the<a>natural numbers</a>progress, their cube roots start to complicate. However, the process of calculating cube roots remains the same. These irrational cube roots can be rounded off to a few decimal places.</p>

14 <strong>Numbers</strong><strong>Cube Root</strong>11 2.22 12 2.29 13 2.35 14 2.41 15 2.47 16 2.52 17 2.57 18 2.62 19 2.67 20 2.71<p><strong>Cube roots from 21 to 30</strong> </p>

15 <p>3 is the only whole<a>cube root</a>within this range. All other cube roots from 21 to 30 are irrational with higher decimal values. Do not worry about the large number of decimal values; you can round them off to a few places after the decimal point.</p>

16 <strong>Numbers</strong><strong>Cube Root</strong>21 2.76 22 2.8 23 2.84 24 2.88 25 2.92 26 2.96 27 3 28 3.04 29 3.07 30 3.1<h3>Explore Our Programs</h3>

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18 <h2>Cube Root from 1 to 30 for Perfect cubes</h2>

17 <h2>Cube Root from 1 to 30 for Perfect cubes</h2>

19 <p>Perfect cubes are numbers formed by multiplying an<a>integer</a>by itself 3 times. Their cube roots are also whole numbers. Between 1 and 30, the only perfect cubes that exist are 1, 8, and 27, with 1, 2, and 3 being their respective cube roots.</p>

18 <p>Perfect cubes are numbers formed by multiplying an<a>integer</a>by itself 3 times. Their cube roots are also whole numbers. Between 1 and 30, the only perfect cubes that exist are 1, 8, and 27, with 1, 2, and 3 being their respective cube roots.</p>

20 <h2>Cube Root from 1 to 30 for Non-Perfect Cubes</h2>

19 <h2>Cube Root from 1 to 30 for Non-Perfect Cubes</h2>

21 <p>A non-perfect cube has a cube root that is not a whole number. Its cube root is always an<a>irrational number</a>. This applies to all integers between 1 and 30 except for 1, 8, and 27.</p>

20 <p>A non-perfect cube has a cube root that is not a whole number. Its cube root is always an<a>irrational number</a>. This applies to all integers between 1 and 30 except for 1, 8, and 27.</p>

22 <h2>How to Calculate Cube Root from 1 to 30</h2>

21 <h2>How to Calculate Cube Root from 1 to 30</h2>

23 <p>The cube roots from 1 to 30 are calculated:</p>

22 <p>The cube roots from 1 to 30 are calculated:</p>

24 <ul><li>By Prime Factorization Method </li>

23 <ul><li>By Prime Factorization Method </li>

25 <li>By Estimation Method</li>

24 <li>By Estimation Method</li>

26 </ul><h3>By Prime Factorization Method</h3>

25 </ul><h3>By Prime Factorization Method</h3>

27 <p>The<a>prime factorization</a>method helps us find perfect cube roots. Follow these steps for calculating the cube roots:</p>

26 <p>The<a>prime factorization</a>method helps us find perfect cube roots. Follow these steps for calculating the cube roots:</p>

28 <p><strong>Step 1</strong>: Compute the prime<a>factors</a>of the number.</p>

27 <p><strong>Step 1</strong>: Compute the prime<a>factors</a>of the number.</p>

29 <p><strong>Step 2:</strong>Group the prime factors in triples.</p>

28 <p><strong>Step 2:</strong>Group the prime factors in triples.</p>

30 <p><strong>Step 3:</strong>After forming triplets, take only one value from each group to find the cube root.</p>

29 <p><strong>Step 3:</strong>After forming triplets, take only one value from each group to find the cube root.</p>

31 <p>Let's solve an example using these steps:</p>

30 <p>Let's solve an example using these steps:</p>

32 <p>Question: Find the cube root of 8</p>

31 <p>Question: Find the cube root of 8</p>

33 <p>Solution: Prime factorization of 8, 8 = 2 × 2 × 2 </p>

32 <p>Solution: Prime factorization of 8, 8 = 2 × 2 × 2 </p>

34 <p>We have one group of triples 23</p>

33 <p>We have one group of triples 23</p>

35 <p>So, 2 is the cube root of 8.</p>

34 <p>So, 2 is the cube root of 8.</p>

36 <h3>By Estimation Method</h3>

35 <h3>By Estimation Method</h3>

37 <p>The<a>estimation</a>method is used for non-perfect cubes so that we can find the approximate root between two nearly perfect cubes. To do so,</p>

36 <p>The<a>estimation</a>method is used for non-perfect cubes so that we can find the approximate root between two nearly perfect cubes. To do so,</p>

38 <p><strong>Step 1:</strong>Find two perfect cubes nearest to the number. The number should lie between them.</p>

37 <p><strong>Step 1:</strong>Find two perfect cubes nearest to the number. The number should lie between them.</p>

39 <p><strong>Step 2:</strong>Make estimations based on how close the numbers are.</p>

38 <p><strong>Step 2:</strong>Make estimations based on how close the numbers are.</p>

40 <p><strong>Step 3:</strong>Refine the estimation by trying different values through<a>multiplication</a>.</p>

39 <p><strong>Step 3:</strong>Refine the estimation by trying different values through<a>multiplication</a>.</p>

41 <p>For example, to estimate 320</p>

40 <p>For example, to estimate 320</p>

42 <p>First, check for the nearest perfect cubes</p>

41 <p>First, check for the nearest perfect cubes</p>

43 <p>23 = 3 and 33 = 27 </p>

42 <p>23 = 3 and 33 = 27 </p>

44 <p> 320 lies between 2 and 3</p>

43 <p> 320 lies between 2 and 3</p>

45 <p> Since 20 is closer to 27, the estimate will be between 2.7 and 2.8</p>

44 <p> Since 20 is closer to 27, the estimate will be between 2.7 and 2.8</p>

46 <p>Now, try 2.73 = 19.683</p>

45 <p>Now, try 2.73 = 19.683</p>

47 <p>2.723 = 20.138</p>

46 <p>2.723 = 20.138</p>

48 <p>2.713= 19.909</p>

47 <p>2.713= 19.909</p>

49 <p>Upon refining these estimates further, we get</p>

48 <p>Upon refining these estimates further, we get</p>

50 <p>∛20 ≈ 2.72 as the answer.</p>

49 <p>∛20 ≈ 2.72 as the answer.</p>

51 <h2>Rules for Finding Cube Root from 1 to 30</h2>

50 <h2>Rules for Finding Cube Root from 1 to 30</h2>

52 <p>Now that we know the two methods of finding cube roots, let's focus on the rules that must be followed while finding cube roots:</p>

51 <p>Now that we know the two methods of finding cube roots, let's focus on the rules that must be followed while finding cube roots:</p>

53 <p><strong>Rule 1: Identifying a Perfect Cube</strong></p>

52 <p><strong>Rule 1: Identifying a Perfect Cube</strong></p>

54 <p>A perfect cube always has a whole number as its cube root. These are also called exact cubes. Between 1 - 30, the perfect cubes are 1, 8, and 27.</p>

53 <p>A perfect cube always has a whole number as its cube root. These are also called exact cubes. Between 1 - 30, the perfect cubes are 1, 8, and 27.</p>

55 <p><strong>Rule 2: Estimating Cube Roots of Non-Perfect Cubes</strong></p>

54 <p><strong>Rule 2: Estimating Cube Roots of Non-Perfect Cubes</strong></p>

56 <p>For numbers that aren't perfect cubes, their cube roots can be estimated by locating the two nearest perfect cubes.</p>

55 <p>For numbers that aren't perfect cubes, their cube roots can be estimated by locating the two nearest perfect cubes.</p>

57 <p><strong>Rule 3: Cube Root Formula</strong></p>

56 <p><strong>Rule 3: Cube Root Formula</strong></p>

58 <p>The cube root of a number y is a number x such that: x = y1/3 Let's say we want to find the cube root of 27, then x = 271/3 = 3</p>

57 <p>The cube root of a number y is a number x such that: x = y1/3 Let's say we want to find the cube root of 27, then x = 271/3 = 3</p>

59 <p><strong>Rule 4: Important Properties of Cube Roots</strong></p>

58 <p><strong>Rule 4: Important Properties of Cube Roots</strong></p>

60 <ul><li>A<a>negative number</a>will have a negative cube. For example, ∛(-8) = -2 because (-2)3 = -8</li>

59 <ul><li>A<a>negative number</a>will have a negative cube. For example, ∛(-8) = -2 because (-2)3 = -8</li>

61 </ul><ul><li>When multiplying or dividing cube roots, you can separate the numbers under the root. For example, ∛(8 × 27) = ∛8 × ∛27 = 2 × 3 = 6 Similarly, for<a>division</a>, ∛(27 ÷ 3) = ∛27 ÷ ∛3 = 3 ÷ 1.44 ≈ 2.08</li>

60 </ul><ul><li>When multiplying or dividing cube roots, you can separate the numbers under the root. For example, ∛(8 × 27) = ∛8 × ∛27 = 2 × 3 = 6 Similarly, for<a>division</a>, ∛(27 ÷ 3) = ∛27 ÷ ∛3 = 3 ÷ 1.44 ≈ 2.08</li>

62 </ul><h2>Tips and Tricks for Cube Root from 1 to 30</h2>

61 </ul><h2>Tips and Tricks for Cube Root from 1 to 30</h2>

63 <p>Picking up a few tips and tricks can help students understand the topic more efficiently. Some helpful tips are:</p>

62 <p>Picking up a few tips and tricks can help students understand the topic more efficiently. Some helpful tips are:</p>

64 <ul><li>Memorize the perfect cubes between 1-30There are only 3 perfect cubes between 1-30, and memorizing them makes calculations like estimation of cube roots easier. So remember that 1, 8, and 27 are perfect cubes.</li>

63 <ul><li>Memorize the perfect cubes between 1-30There are only 3 perfect cubes between 1-30, and memorizing them makes calculations like estimation of cube roots easier. So remember that 1, 8, and 27 are perfect cubes.</li>

65 </ul><ul><li>Use trial cubing for closer estimates.</li>

64 </ul><ul><li>Use trial cubing for closer estimates.</li>

66 </ul><ul><li>Negative numbers can also be cube roots. All negative cubes have negative cube roots and vice versa.</li>

65 </ul><ul><li>Negative numbers can also be cube roots. All negative cubes have negative cube roots and vice versa.</li>

67 </ul><h2>Common Mistakes and How to Avoid Them in Cube Root from 1 to 30</h2>

66 </ul><h2>Common Mistakes and How to Avoid Them in Cube Root from 1 to 30</h2>

68 <p>The concept of cube roots is useful in understanding perfect and non-perfect cubes; however, when a new topic is introduced to students, there are chances of recurring errors. Here is a list of such errors and ways to avoid them:</p>

67 <p>The concept of cube roots is useful in understanding perfect and non-perfect cubes; however, when a new topic is introduced to students, there are chances of recurring errors. Here is a list of such errors and ways to avoid them:</p>

68 + <h2>Download Worksheets</h2>

69 <h3>Problem 1</h3>

70 <p>What is the cube root of 1?</p>

71 <p>Okay, lets begin</p>

72 <p>1</p>

73 <h3>Explanation</h3>

74 <p>∛1 = 1 because 13 = 1</p>

75 <p>Well explained 👍</p>

76 <h3>Problem 2</h3>

77 <p>Estimate the cube root of 2.</p>

78 <p>Okay, lets begin</p>

79 <p>Approximately 1.26</p>

80 <h3>Explanation</h3>

81 <p>Nearest perfect cubes for 2 are 1 and 8.</p>

82 <p>∛2 ≈ 1.26</p>

83 <p>Well explained 👍</p>

84 <h3>Problem 3</h3>

85 <p>Estimate the cube root of 5.</p>

86 <p>Okay, lets begin</p>

87 <p>Approximately 1.71</p>

88 <h3>Explanation</h3>

89 <p>5 lies between perfect cubes 1 and 8, ∛5 ≈ 1.71</p>

90 <p>Well explained 👍</p>

91 <h3>Problem 4</h3>

92 <p>Is 9 a perfect cube? If not, estimate its cube root.</p>

93 <p>Okay, lets begin</p>

94 <p>No, nine is not a perfect cube; its approximate cube root is 2.08</p>

95 <h3>Explanation</h3>

96 <p>We check 23 = 8 and 33 = 27. We can see that 9 is not a perfect cube.</p>

97 <p>So using the estimation method, we see that 9 comes between 8 and 27, </p>

98 <p>After trying different values, we get </p>

99 <p>∛9 ≈ 2.08</p>

100 <p>Well explained 👍</p>

101 <h3>Problem 5</h3>

102 <p>Estimate the cube root of 6.</p>

103 <p>Okay, lets begin</p>

104 <p>Approximately 1.82</p>

105 <h3>Explanation</h3>

106 <p>6 lies between the perfect cubes, 8 and 1, so, ∛6 ≈ 1.82</p>

107 <p>Well explained 👍</p>

108 <h2>FAQs on Cube Root from 1 to 30</h2>

109 <h3>1.What is a cube root?</h3>

110 <p>A cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, 3 is the cube root of 27.</p>

111 <h3>2.How is the cube root denoted?</h3>

112 <p>The cube root is denoted by the<a>symbol</a>3√</p>

113 <h3>3.How many perfect cubes between 1-30?</h3>

114 <p>1, 8, and 27 are the three perfect cubes between 1 and 30.</p>

115 <h3>4.What is the easiest method to find cube roots of small numbers?</h3>

116 <p>Prime factorization and estimation methods are commonly used to find the cube roots of small numbers.</p>

117 <h3>5.Why is ∛2 not a whole number?</h3>

118 <p>∛2 is not a whole number because it is irrational and cannot be written as a whole or even as a simple<a>fraction</a>.</p>

119 <h2>Important Glossaries for Cube Root from 1 to 30</h2>

120 <ul><li><strong>Irrational number:</strong>Numbers that cannot be written as simple fractions or whole numbers are irrational numbers.</li>

121 </ul><ul><li><strong>Trial cubing:</strong>The method of trying different numbers by cubing them to find a cube root is known as trial cubing.</li>

122 </ul><ul><li><strong>Exact cube:</strong>Exact cube is just another synonym for a perfect cube.</li>

123 </ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

124 <p>▶</p>

125 <h2>Jaskaran Singh Saluja</h2>

126 <h3>About the Author</h3>

127 <p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>

128 <h3>Fun Fact</h3>

129 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>