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Last updated on November 30th, 2024
The cube root of 121 is the value that, when multiplied by itself three times (cubed), gives the original number 121. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, designing structures, density and mass, field of engineering etc.
The cube root of 121 is 4.94608744325. The cube root of 121 is expressed as ∛121 in radical form, where the “ ∛ “ sign” is called the “radical” sign. In exponential form, it is written as (121)1/3. If “m” is the cube root of 121, then, m3=121. Let us find the value of “m”.
We can find cube root of 121 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 121.
Step 1: Let a=121. Let us take x as 4, since 43=64 is the nearest perfect cube which is less than 121.
Step 2: Apply the formula. ∛121≅ 4((43+2×121) / (2(4)3+121))= 4.92
Hence, 4.92 is the approximate cubic root of 121.