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Last updated on November 30th, 2024
The cube root of 192 is the value that, when multiplied by itself three times (cubed), gives the original number 192. Do you know? Cube roots apply to our real life also, like that for measuring volume and scaling, density and mass calculation, etc.
The cube root of 192 is 5.76899828123. The cube root of 192 is expressed as ∛192 in radical form, where the “∛" sign is called the “radical” sign. In exponential form, it is written as (192)â…“. If “m” is the cube root of 192, then, m3=192. Let us find the value of “m”.
The cube root of 192 is expressed as 4∛3 as its simplest radical form, since
192 = 2×2×2×2×2×2×3
∛192 = ∛(2×2×2×2×2×2×3)
Group together three same factors at a time and put the remaining factor under the ∛ .
∛192= 4∛3
We can find cube root of 192 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 ∛a≅ 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 192.
Step 1: Let a=192. Let us take x as 5, since, 125 is the nearest perfect cube which is less than 192.
Step 2: Apply the formula. ∛192≅ 5((53+2×192) / (2(5)3+192))=5.757
Hence, 5.757 is the approximate cubic root of 192.