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Last updated on November 30th, 2024
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.