Last updated on May 26th, 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.
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”.
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.
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.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Find β12/ β6
β12/ β6
= 2.289 / 1.817
= 2289/1817
=1.26
Answer: 1.26
We know that the cubic root of 6 is 1.817, hence dividing β12 by β6.
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
We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
Subtract β12 - β8, β27-β12
β12-β8= 2.289–2= 0.289
β27-β12 = 3-2.289 = 0.711
Answer: 0.289, 0.711
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.
What is β(12Β²) ?
(122) = β144
= 5.241…
Answer: 5.241…
We first found the square value of 12, which is 144, and then found out the cube root of 144.
Find β(12+15).
β(12+15)
= β27
=3
Answer: 3
Simplified the expression, and found out the cubic root of the result.
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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