Using Newton-Raphson’s method, find the cube root of 24?

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2.884

3.256

5.231

4.526

answer is A.

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Detailed Solution

Concept: Newton – Raphson’s method is an advanced tool using concepts of calculus to determine cube roots (any root of a no.). It uses approximation as a tool to pinpoint the closest value of answers. When the solution starts iterating we stop to solve further and accept the last iterated value as the answer.
To find the cube root of 24 using Newton - Raphson method, we need to solve

Notice

Therefore the cube root of 24 is slightly less than 3 .
We have

Let us start estimating the root

Let the first estimation be a

(slightly less than 3 )
Hence the subsequent estimates will be

and

Therefore

Now

Hence the cube root of 24 is 2.884
Hence, option 1 is correct.

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