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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 3000, and its examples.
The cube root of 3000 is the value which, when multiplied by itself three times (cubed), gives the original number 3000.
The cube root of 3000 is 14.4224957031. The cube root of, 3000 is expressed as ∛3000 in radical form, where the “ ∛ ” sign” is called the “radical” sign. In exponential form, it is written as (3000)⅓. If “m” is the cube root of 3000, then, m3=3000. Let us find the value of “m”.
We can find cube roots of 3000 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, 3000.
Step 1: Let a=3000. Let us take x as 14, since 143=2744 is the nearest perfect cube which is less than 3000.
Step 2: Apply the formula. ∛3000≅ 14((143+2×3000) / (2(14)3+3000)) = 14.42…
Hence, 14.42… is the approximate cubic root of 3000.
2) The cube root of a negative number is also negative.
3) If the cube root of a number is a whole number, then that original number is said to be perfect cube