Cube Root Of 21
2026-02-28 01:13 Diff
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Last updated on August 5, 2025

The cube root of a number is a value that when multiplied by itself three times gives back the original number. We apply the function of cube roots in the fields of engineering, designing, financial mathematics, and many more. Let's learn more about the cube root of 21.

What Is The Cube Root Of 21?

The cube root can be classified into two categories: perfect cubes and non-perfect cubes. For example, the cube root of 27 is 3 which is a whole number, making it a perfect cube. However, the cube root of 21 is not a whole number. The cube root of 21 is approximately 2.759.

The cube root of 21 is represented using the radical sign as ∛21, and can also be written in exponential form as 211/3. The prime factorization of 21 is 3 × 7. It is also an irrational number where ∛21 cannot be expressed in the form of p/q where both p and q are integers and q ≠ 0. 
 

Finding The Cube Root Of 21

Finding cube roots for perfect cubes is easy, but for non-perfect cubes, the process can be a bit tricky. For non-perfect cubes, we can use Halley’s method. Let’s explore how this method helps us find the cube root of 21.
 

Cube Root Of 21 By Halley’s Method

Halley’s method is a step-by-step way to find the cube root of a non-perfect cube number. Here, we will find the value of ‘a’ where a3 is the non-perfect cube


∛a≅  x (x3+2a)/ (2x3+a) is the formula used in this method. 

As 21 is a non-perfect cube number, it lies between the two perfect cube numbers. Here, ‘a’ lies between 8 (23) and 27 (33). 


By applying Halley’s Method, we get.


Step 1: Let the number ‘a’ = 21. Start by taking ‘x’ = 2, as 8 (∛8 = 2) is the nearest perfect cube which is closer to 21


Step 2: Apply the value of ‘a=21’ and ‘x=2’ in the formula: 


 ∛a≅  x (x3+2a)/ (2x3+a)

Step 3: The formula will be, 


 ∛21 ≅  2 (23+2*21) /(2*23+21)

Step 4: After simplifying, we get the cube root of 21 as 2.7589.

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Common Mistakes And How To Avoid Them In Cube Root Of 21

Making mistakes while learning cube roots is common. Let’s look at some common mistakes kids might make and how to fix them.
 

Download Worksheets

Problem 1

What is the cube root of 111?

Okay, lets begin

The cube root of 111 is 4.806.

Explanation

The cube root of 111 is 4.806.

It is a direct question that is very easy to solve, as we don’t have much to calculate.

All we need to do is find the cube root of the given number.
 

Well explained 👍

Problem 2

What is the ∛(30+1)?

Okay, lets begin

 The cube root of the given number is 3.141.

Explanation

The first step is to add the given numbers in the bracket.

Once we add these two given numbers, we find the cube root of that number.

Well explained 👍

Problem 3

What is the solution for ∛1000?

Okay, lets begin

The cube root of 1000 is 10.
 

Explanation

We can use the method of prime factorization to find the cube root of a perfect cube easily.

Let us first bring the number to its primal form and then if the primal form has the same numbers as a group of 3, then it is the cube of a number.

Well explained 👍

Problem 4

What is √999?

Okay, lets begin

The solution to this question is 31.6069612586.
 

Explanation

The cube root of 999 is 31.607.

It is a direct question that is very easy to solve, as we don’t have much to calculate.

All we need to do is find the cube root of the given number.

Well explained 👍

Problem 5

What is the √(100)²?

Okay, lets begin

The solution to this question is 100.

Explanation

A simple way to understand this is, If there is a “x2” inside a square root, the square, and the root will get canceled out.

And the number remaining will be the answer.

Well explained 👍

FAQs For Cube Root Of 21

1.What is the cube root of a negative number?

The cube root of a negative number can be negative only if the power of the given number is odd. For example, ∛(-2)2=1.587 and ∛(-2)3= -2.
 

2.How to solve √30?

Prime factorization, Long Division, and Estimation, are 3 ways to solve √30. The square root of 30 is ±5.477.
 

3.What is the square root of 52 in the simplest form?

The square root of 52, simplified, is expressed as 2√13, in its simplest form.
 

4.Is 21 a perfect square?

21 is not a perfect square number. This is because there is no whole number that when squared will give us 21.
 

5.Is √21 rational?

 The square root of 21 is not a rational number, since it can not be expressed as a p/q form. 
 

Important Glossaries for Cube Root of 21

  • Fraction: It is a way to show a part of something. For example, in the fraction 2/5 , it means you have 2 out of 5 equal parts. 
  • Exponent: It is a smaller number that shows us how many times we multiply the number by itself. For example, in 33, 3 is the exponent, which means we multiply 3 three times.
  • Non-terminating: Numbers that go on infinite times without an end. For example, 3.1415926535
     

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