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Last updated on November 30th, 2024
The cube root of 250 is the value which, when multiplied by itself three times (cubed), gives the original number 250. 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 250 is 6.29960524947. The cube root of 250 is expressed as β250 in radical form, where the “ β “ sign" is called the “radical” sign. In exponential form, it is written as (250)1/3. If “m” is the cube root of 250, then, m3=250. Let us find the value of “m”.
The cube root of 250 is expressed as 5β2 as its simplest radical form, since
250 = 5×5×5×2
β250 = β(5×5×5×2)
Group together three same factors at a time and put the remaining factor under β .
β250= 5β2
We can find cube roots of 250 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 250.
Step 1: Let a=250. Let us take x as 6, since 63=216 is the nearest perfect cube which is less than 250.
Step 2: Apply the formula. β250≅ 6((63+2×250) / (2(6)3+250))= 6.29…
Hence, 6.29… is the approximate cubic root of 250.