# Compute the fourth root of 20 using Newton-Raphson interation

Not what you're looking for? Search our solutions OR ask your own Custom question.

Give the Newton-Raphson iteration scheme for computing the pth power of a number.

Specialize this to computing the fourth root of 20. You can take the initial guess to be 2.

At each iteration, state the number of correct digits.

Â© BrainMass Inc. brainmass.com December 16, 2022, 2:36 pm ad1c9bdddfhttps://brainmass.com/math/numerical-analysis/compute-fourth-root-20-newton-raphson-interation-647581

#### Solution Preview

Given y, we want to compute x = y^p. This means that x satisfies the equation:

x^(1/p) = y ----->

x^q - y = 0

where q = 1/p

We can then apply Newton-Raphson iteration. In general, given an equation f(x) = 0 and

initial guess x_0, this yields the sequence of approximants to the solution of:

x_{n+1} = x_n - ...

#### Solution Summary

The given answer assumes familiarity with Newton-Raphson iteration. It gives a detailed answer using the Newton-Raphson formula.

$2.49