Cube Root from 1 to 30
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Last updated on September 26, 2025

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.

Cube Root from 1 to 30

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

Cube Root from 1 to 30 chart

The cube 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.

List of Cube Roots from 1 to 30

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

Cube roots from 1 to 10

The cube roots between 1 and 10, including whole numbers as well as decimals, are given below:

Number Cube Root 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

Cube roots from 11 to 20

As the natural numbers 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.

Numbers Cube Root 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

Cube roots from 21 to 30
 

3 is the only whole cube root 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.

Numbers Cube Root 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

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Cube Root from 1 to 30 for Perfect cubes

Perfect cubes are numbers formed by multiplying an integer 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.

Cube Root from 1 to 30 for Non-Perfect Cubes

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

How to Calculate Cube Root from 1 to 30

The cube roots from 1 to 30 are calculated:

  • By Prime Factorization Method
     
  • By Estimation Method

By Prime Factorization Method

The prime factorization method helps us find perfect cube roots. Follow these steps for calculating the cube roots:

Step 1: Compute the prime factors of the number.

Step 2: Group the prime factors in triples.

Step 3: After forming triplets, take only one value from each group to find the cube root.

Let's solve an example using these steps:

Question: Find the cube root of 8

Solution: Prime factorization of 8, 8 = 2 × 2 × 2 

We have one group of triples 23

So, 2 is the cube root of 8.

By Estimation Method

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

Step 1: Find two perfect cubes nearest to the number. The number should lie between them.

Step 2: Make estimations based on how close the numbers are.

Step 3: Refine the estimation by trying different values through multiplication.

For example, to estimate 320

First, check for the nearest perfect cubes

23 = 3 and 33 = 27 

 320 lies between 2 and 3

  Since 20 is closer to 27, the estimate will be between 2.7 and 2.8

Now, try 2.73 = 19.683

2.723 = 20.138

2.713= 19.909

Upon refining these estimates further, we get

∛20 ≈ 2.72 as the answer.

Rules for Finding Cube Root from 1 to 30

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:

Rule 1: Identifying a Perfect Cube

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.

Rule 2: Estimating Cube Roots of Non-Perfect Cubes

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

Rule 3: Cube Root Formula

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

Rule 4: Important Properties of Cube Roots

  • A negative number will have a negative cube. 
    For example, ∛(−8) = −2 because (−2)3 = −8
  • 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 division, ∛(27 ÷ 3) = ∛27 ÷ ∛3 = 3 ÷ 1.44 ≈ 2.08

Tips and Tricks for Cube Root from 1 to 30

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

  • 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.
  • Use trial cubing for closer estimates.
  • Negative numbers can also be cube roots. All negative cubes have negative cube roots and vice versa.

Common Mistakes and How to Avoid Them in Cube Root from 1 to 30

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:

Download Worksheets

Problem 1

What is the cube root of 1?

Okay, lets begin

1

Explanation

∛1 = 1 because 13 = 1

Well explained 👍

Problem 2

Estimate the cube root of 2.

Okay, lets begin

Approximately 1.26

Explanation

Nearest perfect cubes for 2 are 1 and 8.

∛2 ≈ 1.26

Well explained 👍

Problem 3

Estimate the cube root of 5.

Okay, lets begin

Approximately 1.71

Explanation

5 lies between perfect cubes 1 and 8, ∛5 ≈ 1.71

Well explained 👍

Problem 4

Is 9 a perfect cube? If not, estimate its cube root.

Okay, lets begin

No, nine is not a perfect cube; its approximate cube root is 2.08

Explanation

We check 23 = 8 and 33 = 27. We can see that 9 is not a perfect cube.

So using the estimation method, we see that 9 comes between 8 and 27, 

After trying different values, we get 

∛9 ≈ 2.08

Well explained 👍

Problem 5

Estimate the cube root of 6.

Okay, lets begin

Approximately 1.82

Explanation

6 lies between the perfect cubes, 8 and 1, so, ∛6 ≈ 1.82

Well explained 👍

FAQs on Cube Root from 1 to 30

1.What is a cube root?

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.

2.How is the cube root denoted?

The cube root is denoted by the symbol 3√

3.How many perfect cubes between 1-30?

1, 8, and 27 are the three perfect cubes between 1 and 30.

4.What is the easiest method to find cube roots of small numbers?

Prime factorization and estimation methods are commonly used to find the cube roots of small numbers.

5.Why is ∛2 not a whole number?

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

Important Glossaries for Cube Root from 1 to 30

  • Irrational number: Numbers that cannot be written as simple fractions or whole numbers are irrational numbers.
  • Trial cubing: The method of trying different numbers by cubing them to find a cube root is known as trial cubing.
  • Exact cube: Exact cube is just another synonym for a perfect cube.

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Jaskaran Singh Saluja

About the Author

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.

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: He loves to play the quiz with kids through algebra to make kids love it.