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Last updated on November 30th, 2024
The cube root of 128 is the value that, when multiplied by itself three times (cubed), gives the original number 128. 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 128 is 5.03968419958. The cube root of 128 is expressed as β128 in radical form, where the ββ" sign is called the βradicalβ sign. In exponential form, it is written as (128)β
. If βmβ is the cube root of 128, then, m3=128. Let us find the value of βmβ.
The cube root of 128 is expressed as 4β2 as its simplest radical form,
since 128 = 2Γ2Γ2Γ2Γ2Γ2Γ2
β128 = β(2Γ2Γ2Γ2Γ2Γ2Γ2)
Group together three same factors at a time and put the remaining factor under the β .
β128= 4β2
We can find cube root of 128 through a method, named as, Halleyβs Method. Let us see how it finds the result.
Now, what is Halleyβs 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 βxβ.
Formula is βaβ
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 Halleyβs method on the given number 128.
Step 1: Let a=128. Let us take x as 5, since, 53=125 is the nearest perfect cube which is less than 128.
Step 2: Apply the formula. β128β
5((53+2Γ128) / (2(5)3+128))= 5.039β¦
Hence, 5.039β¦ is the approximate cubic root of 128.