Cube Root of 12
2026-02-28 11:49 Diff
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Last updated on August 5, 2025

The cube root of 12 is the value which, when multiplied by itself three times (cubed), gives the original number 12. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.

What Is the Cubic Root of 12?

The cube root of 12 is 2.28942848511. The cube root of 12 is expressed as ∛12 in radical form, where the “ ∛ “  sign is called the “radical” sign. In exponential form, it is written as (12)1/3.  If “m” is the cube root of 12, then, m3=12.  Let us find the value of “m”.
 

Finding the Cubic Root of 12

The cube root of 12 is expressed as ∛12 as its simplest radical form, since 12 = 2×2×3


∛12 = ∛(2×2×3)


Group together three same factors at a time and put the remaining factor under ∛.


∛12= ∛12 


 We can find cube root of 12 through a method, named Halley’s Method. Let us see how it finds the result.
 

Cubic Root of 12 By Halley’s Method

Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.


Formula is ∛a≅ x((x3+2a) / (2x3+a)), where 


a=given number whose cube root you are going to find


x=integer guess for the cubic root


 Let us apply Halley’s method on the given number 12.


Step 1: Let a=12. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 12.


Step 2: Apply the formula.  ∛12≅ 2((23+2×12) / (2(2)3+12))= 2.285…


Hence, 2.285… is the approximate cubic root of 12.
 

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Common Mistakes and How to Avoid Them in the Cube Root of 12

Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
 

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Problem 1

Find ∛12/ ∛6

Okay, lets begin

∛12/ ∛6

= 2.289 / 1.817

= 2289/1817

=1.26


Answer: 1.26
 

Explanation

We know that the cubic root of 6 is 1.817, hence dividing  ∛12 by ∛6.

Well explained 👍

Problem 2

The Volume of a cube is 12 cubic centimeters, find the length of one side of the cube.

Okay, lets begin

We know that, (side of a cube)3=Volume of a cube


⇒side of the cube =  ∛(Volume of the cube)


⇒side of the cube = ∛12


⇒ side of the cube = 2.289 cm


Answer: 2.289 cm
 

Explanation

We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
 

Well explained 👍

Problem 3

Subtract ∛12 - ∛8, ∛27-∛12

Okay, lets begin

∛12-∛8= 2.289–2= 0.289


∛27-∛12 = 3-2.289 = 0.711


Answer:  0.289, 0.711
 

Explanation

We know that the cubic root of 8 is 2, hence subtracting  ∛8 from ∛12. Applying the same for the next one, we know that the cubic root of 27 is 3, hence subtracting ∛12 from ∛27.
 

Well explained 👍

Problem 4

What is ∛(12²) ?

Okay, lets begin

(122) = ∛144

= 5.241… 


Answer: 5.241… 
 

Explanation

We first found the square value of 12, which is 144, and then found out the cube root of 144.
 

Well explained 👍

Problem 5

Find ∛(12+15).

Okay, lets begin

 ∛(12+15)

= ∛27

=3


Answer: 3
 

Explanation

Simplified the expression, and found out the cubic root of the result. 
 

Well explained 👍

FAQs on 12 Cubic Root

1.What is 3√12 simplified ?

 3√12

= 3√(2×2×3)

= 3×2√3

=6√3.
 

2.Can the ∛12 be simplified ?

 ∛12 cannot be simplified further. Its simplest radical form is ∛12, since on Prime Factorization, it is not possible to make a group of three for any of the prime factors 12 has.
 

3.What will be the cube of 12?

4.How is √12 written as 3√2 ?

12= 2×2×3


√12 = √(2×2×3)


√12 = 2√3


So, on prime factorization, √12 can be written as 2√3.
 

5.How is √12 irrational?

 √12 is irrational because, √12=2.28942848511, where, 2.28942848511 is an irrational number, since it cannot be obtained by dividing two integers and cannot be written in the form p/q, where p and q are integers.
 

Important Glossaries for Cubic Root of 12

  • Integers - Numbers which are positive, negative, or zero, and with which we can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. All integers are rational numbers. Ex:  1, 2, 5,6,8, -9, -12,-15 etc.
  • Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. These cannot be in fractional or decimal form. 
  • Square root -The square root of a number is a value, which, on multiplication by itself, gives the original number, such that √x = y, where y×y = x.
  • Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
  • Approximation - Finding out a value which is nearly correct, but not perfectly correct, as if the approximate value is just near and close the original value.
     

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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.