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Last updated on October 1st, 2024
The cube root of 16 is the value that, when multiplied by itself three times (cubed), gives the original number 16. 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 16 is 2.51984209979. The cube root of 16 is expressed as β16 in radical form, where the “ β ” sign is called the “radical” sign. In exponential form, it is written as (16)β . If “m” is the cube root of 16, then, m3=16. Let us find the value of “m”.
The cube root of 16 is expressed as 2β2 as its simplest radical form,
since 16 = 2×2×2×2
β16 = β(2×2×2×2)
Group together three same factors at a time and put the remaining factor under the β .
β16= 2β2
We can find cube root of 16 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 16.
Step 1: Let a=16. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 16.
Step 2: Apply the formula. β16≅ 2((23+2×16) / (2(2)3+16))= 2.5
Hence, 2.5 is the approximate cubic root of 16.