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Last updated on November 30th, 2024
The cube root of 243 is the value that, when multiplied by itself three times (cubed), gives the original number 243. 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 243 is 6.24025146916. The cube root of 243 is expressed as β243 in radical form, where the “ β “ sign is called the “radical” sign. In exponential form, it is written as (243)1/3. If “m” is the cube root of 243, then, m3=243. Let us find the value of “m”.
The cube root of 243 is expressed as 3β9 as its simplest radical form, since
243 = 3×3×3×3×3
β243 = β(3×3×3×3×3)
Group together three same factors at a time and put the remaining factor under β .
β243= 3β9
We can find cube root of 243 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 243.
Step 1: Let a=243. Let us take x as 6, since, 63=216 is the nearest perfect cube which is less than 243.
Step 2: Apply the formula. β243≅ 6((63+2×243) / (2(6)3+243))= 6.24
Hence, 6.24 is the approximate cubic root of 243.