Question

Find a positive value of (17)^1/3 correct to six decimal places by newton-raphson method

Answer 1

Positive value of (17)^1/3 to six decimal places is 2.817121

Given;

Term to be solved = (17)^1/3

To Find;

Positive value of (17)^1/3 to six decimal places using the Newton-Raphson method.

Solution;

The Newton-Raphson method is a numerical method used to find the roots of a function. To find a positive value of (17)^(1/3) correct to six decimal places, we can use the Newton-Raphson method as follows:

Start with an initial guess for the root. For example, x0 = 2 (since it is a positive value of (17)^(1/3))

We need to find the derivative of x^3 - 17 = 0 to use in the Newton Raphson method.

f'(x) = 3x^2

Calculate the next approximation, x1, using the formula:

x1 = x0 - (f(x0) / f'(x0))

x1 = x0 - ((x0^3 - 17) / (3x0^2))

Repeat step 3, using x1 as the new value of x0, until the desired level of accuracy is reached.

x1 = 2.81712059

x2 = 2.81712059 and it is accurate up to 6 decimal places.

So the positive value of (17)^(1/3) correct to six decimal places is 2.817121

It's important to note that, this method requires the function to be differentiable and one needs to have good guess to get the accurate results.

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