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Last updated on November 30th, 2024
The cube root of 25 is the value which, when multiplied by itself three times (cubed), gives the original number 25. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, creating unique digital art etc.
The cube root of 25 is 2.92401773821. The cube root of 25 is expressed as ∛25 in radical form, where the “ ∛ “ sign is called the “radical” sign. In exponential form, it is written as (25)1/3. If “m” is the cube root of 25, then, m3=25. Let us find the value of “m”.
The Prime Factorization of 25 is 5×5, so, the cube root of 25 is expressed as ∛25 as its simplest radical form. We can find the cube root of 25 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 ∛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 25.
Step 1: Let a=25. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 25.
Step 2: Apply the formula. ∛25≅ 2((23+2×25) / (2(2)3+25))= 2.82…
Hence, 2.82… is the approximate cubic root of 25.