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Last updated on October 1st, 2024
The cube root of 24 is the value that, when multiplied by itself three times (cubed), gives the original number 24. 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 24 is 2.88449914061. The cube root of 24 is expressed as β24 in radical form, where the “ β “ sign is called the “radical” sign. In exponential form, it is written as (24)β
. If “m” is the cube root of 24, then, m3=24. Let us find the value of “m”.
The cube root of 24 is expressed as 2β3 as its simplest radical form,
since 24 = 2×2×2×3
β24 = β(2×2×2×3)
Group together three same factors at a time and put the remaining factor under the β .
β24= 2β3
We can find cube root of 24 through a method, named as, 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 24.
Step 1: Let a=24. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 24.
Step 2: Apply the formula. β24≅ 2((23+2×24) / (2(2)3+24))= 2.8
Hence, 2.8 is the approximate cubic root of 24.