279 LearnersLast updated on May 26th, 2025
Cube Root of 12
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 β12 in radical form, where the “ β “ 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 β12 as its simplest radical form, since 12 = 2×2×3
β12 = β(2×2×3)
Group together three same factors at a time and put the remaining factor under β.
β12= β12
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 Halleyβs 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 βa≅ 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. β12≅ 2((23+2×12) / (2(2)3+12))= 2.285…
Hence, 2.285… is the approximate cubic root of 12.
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.
Mistake 1
Children get confused of the concept of cube root with that of square root.
The Cube root of 12 is β12, and the square root of 12 is √12. Understand the definition of Cube roots and square root.
Mistake 2
Misidentifying prime numbers with composite numbers while doing prime factorization to find cube roots.
While prime factorization, make sure you know which numbers areprime and which are not. Have a clear vision on prime numbers and composite numbers before applying Prime Factorization method.
Mistake 3
Applying exponent rules incorrectly when finding cube roots.
β12 is not same as 123. β12 =2.285 … and 123=1728.
Mistake 4
Students often calculate mentally the value of cube roots
Students can use Prime factorization method or Halley’s method to find out the approximate value for cube roots.
Mistake 5
Not checking for perfect cubes, like that of 8, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from 1 to 100.
Cube Root of 12 Examples
Problem 1
Find β12/ β6
β12/ β6
= 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 β12 by β6.
Problem 2
The Volume of a cube is 12 cubic centimeters, find the length of one side of the cube.
We know that, (side of a cube)3=Volume of a cube
⇒side of the cube = β(Volume of the cube)
⇒side of the cube = β12
⇒ 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.
Problem 3
Subtract β12 - β8, β27-β12
β12-β8= 2.289–2= 0.289
β27-β12 = 3-2.289 = 0.711
Answer: 0.289, 0.711
Explanation
We know that the cubic root of 8 is 2, hence subtracting β8 from β12. Applying the same for the next one, we know that the cubic root of 27 is 3, hence subtracting β12 from β27.
Problem 4
What is β(12Β²) ?
(122) = β144
= 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.
Problem 5
Find β(12+15).
β(12+15)
= β27
=3
Answer: 3
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 12 Cubic Root
1.What is 3β12 simplified ?
2.Can the β12 be simplified ?
3.What will be the cube of 12?
4.How is β12 written as 3β2 ?
5.How is β12 irrational?
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.
