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Last updated on November 30th, 2024
We will learn the cube root concept to use it on other mathematical topics like algebra, mensuration, geometry, trigonometry, etc. So, it is as important as learning square roots. Let us now see how we can obtain the cube root value of 18, and its examples.
The cube root of 18 is the value which, when multiplied by itself three times (cubed), gives the original number 18. The cube root of 18 is 2.62074139421. The cube root of 18 is expressed as β18 in radical form, where the “ β ” sign” is called the “radical” sign. In exponential form, it is written as (18)β
. If “m” is the cube root of 18, then, m3=18. Let us find the value of “m”.
We can find cube root of 18 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 18.
Step 1: Let a=18. Let us take x as 2, since 23=8 is the nearest perfect cube which is less than 18.
Step 2: Apply the formula. β18≅ 2((23+2×18) / (2(2)3+18))= 2.59…
Hence, 2.59… is the approximate cubic root of 18.