Cube root of 27
2026-02-28 23:30 Diff
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Last updated on August 5, 2025

Cube root of 27 is nothing but the number which when multiplied by it for 3 times gives the result as 27. They are utilized in loudspeaker technology as well as in pharmacology for determining the dosage of a medicine on the basis of patient body weight. Cube root of 27 is nothing but the number which when multiplied by it for 3 times gives the result as 27. They are utilized in loudspeaker technology as well as in pharmacology for determining the dosage of a medicine on the basis of patient body weight.

What is the cube root of 27?

The cube root of 27 is 3. ∛27 — Radical notation for the cube root of 27. This can just be written as (27)⅓ in simpler terms.
 

Finding the cube root of 27

To calculate The Cube Root Of 27 we Have Two Methods Mainly


i) Prime Factorisation Method.


ii) Subtraction method.
 

Cube root of 27 by Prime Factorization method

Finding a cube root of 27 through the Prime Factorization method involves determining the factor of 27.


Step 1 — Find the prime factors of 27. 
 

So the prime factor of 27 is 3×3×3


Step 2 — Group the factors of 27 together in a group of 3(i.e., power of 3).


Step 3– Here, we get the factor 3 in the power of 3, i.e., 33 or 3×3×3 

The cube root of 27 can be written as ∛27 = ∛(3×3×3) = 3 

Therefore, the cube root of 27 is 3.

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Cube root of 27 by Subtraction method

This method involves subtracting successive odd numbers repeatedly. The list of odd numbers that should be subtracted successively are →

1,7,19,37,61,91,127,169,217,331,397 … This iteration will continue till we get a zero. 

Step 1 — Subtract the 1st odd number : 27–1 = 26 


Step 2 — Subtract the next odd number: 26–7 = 19


Step 3 — Subtract the next odd number: 19–19 = 0


Here, the subtraction took place in three steps to reach zero.


Hence, the cube root of 27 is 3.

27-1 = 26


26-7 = 19


19-19 = 0

Common Mistakes and How to Avoid Them in the Cube Root of 27

In finding out the cubic root for 27, the common mistakes happen so lets see some of the mistakes and how to solve them.
 

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Problem 1

The Volume of a cube is 27 cubic centimeters, find the length of one side of the cube.

Okay, lets begin

Answer:  3 centimeters

Explanation

Volume of cube = a3, where a is the side length


Equation:  a3 = 27


Apply the cube root:  a = ∛27


Simplify: a = 3 
 

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Problem 2

Is the cube root of a positive number always positive?

Okay, lets begin

Answer:    Yes
 

Explanation

This is because a negative number multiplied by itself (like three) will always result in a negative number. For example, -3✖-3✖-3 = -27
 

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Problem 3

What is the cube root of -27?

Okay, lets begin

Answer: -3
 

Explanation

 -3 multiplied by itself three times equals -27: -3 x -3 x -3 = -27.
 

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Problem 4

Is 27 a perfect cube?

Okay, lets begin

Yes
 

Explanation

27 can be expressed as 3✖3✖3 = 27. Multiplying the digit 3, thrice, results in 27 which means 27 is a perfect cube.  
 

Well explained 👍

Problem 5

What is the relationship between the cube root 27 and the cube of a number?

Okay, lets begin

The cube root and the cube of a number are inverse operations. 

Explanation

The cube root of 27 is 3. If you cube 3, you get 27.
 

Well explained 👍

FAQs on 27 Cube Root

1.What is √27?

2.List the factors of 27.

 The factors of 27 would be 1, 3, 9, and 27.  

3.How will you solve √27 from 3?

First you need to find the √27.


√27 = √(9 × 3) =  √9 × √3 = 3√3  


Therefore, 3√27 = 3x (3√3) = 9√3. 
 

4.What is the cube root of 64?

 The cube root of 64 is 4.
 

5. Is 300 perfect cube?

Important Glossaries for Cube Root of 27

  • Integers:These are numbers that can be positive, negative, or zero, but can never be fractions. All the above Engineering mathematics dido contents can be done with Integers and those includes the four basic arithmetic operations. The examples of integers are, 1, 2, 5,8, -9, -12 et cetera.
  • Whole numbers:Zero and all of the natural numbers collectively known as whole numbers are also a part of the number system that extends in positive direction from zero and goes towards infinity.
  • Square root:A square root of a number is defined as a value which when multiplied by itself will give the original figure as the resultant.

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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.

Fun Fact

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