0

# What is the cube root of 12 by newton raphson formula?

Updated: 2/11/2024

Wiki User

7y ago

The N-R method is an iterative method whereby:

x{n+!} = x{n} - f(x{n})/f'(x{n})

and repeat until |x{n+1} - x{n}| < ε for some small number ε which gives the level of accuracy required.

In this case: f(x) = x³ - 12

→ f'(x) = 3x²

→ x{n+1} = x{n} - (x{n}³-12)/(3x{n}²)

The cube root of 12 lies between 2 (2³ = 8) and 3 (3³ = 27), so pick a value close to 2, say 2.1 as an initial guess then:

x{0} = 2.1

→ x{1} = 2.1 - (2.1³ - 12)/(3×2.1²) ≈ 2.3070

→ x{2} = 2.3070 - (2.3070³ - 12)/(3×2.3070²) ≈ 2.2896

and so on.

with this |x{7} - x{6}| < 1×10^-10 → cube root 12 to 9 dp is 2.289428485.

Wiki User

7y ago

Suryakant Panda

Lvl 1
1y ago

Wiki User

7y ago

If you start from n(0) = 2.5, then n(4) = n(5) = 2.28942848510666 to 14 dp.

Kalif Ahmed

Lvl 2
7mo ago

Cube root 12 Newton raphso

Earn +20 pts
Q: What is the cube root of 12 by newton raphson formula?
Submit
Still have questions?
Related questions

### Why it is advantageous to combine Newton Raphson method and Bisection method to find the root of an algebraic equation of single variable?

An improved root finding scheme is to combine the bisection and Newton-Raphson methods. The bisection method guarantees a root (or singularity) and is used to limit the changes in position estimated by the Newton-Raphson method when the linear assumption is poor. However, Newton-Raphson steps are taken in the nearly linear regime to speed convergence. In other words, if we know that we have a root bracketed between our two bounding points, we first consider the Newton-Raphson step. If that would predict a next point that is outside of our bracketed range, then we do a bisection step instead by choosing the midpoint of the range to be the next point. We then evaluate the function at the next point and, depending on the sign of that evaluation, replace one of the bounding points with the new point. This keeps the root bracketed, while allowing us to benefit from the speed of Newton-Raphson.

### When formula involves cube root?

Then you calculate the cube root!

### How do you get the cubed root of 99?

You can either use a calculator or a numerical method such as Newton-Raphson (for which you will require a calculator!)

### How do you compute a square root?

Square roots are computed using the Babylonian method, calculators, Newton's method, or the Rough estimation method. * * * * * Or the Newton-Raphson method.

### What does Newton's law of Raphson state?

Newton's method, also known as Newton-Raphson method, is an iterative technique for finding the roots of a real-valued function. It starts with an initial guess and refines the estimate in each iteration by using the derivative of the function. The method is based on the principle that a function can be approximated locally by a linear function at a root.

### What is newton-raphson formula for finding roots of non linear equations?

The Newton-Raphson method works if the equations are differentiable over the domain. Let f(x) be the non-linear equation and f'(x) by its derivative [with respect to x]. Start with a reasonable guess at the answer, x0. Then calculate the sequence xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, &acirc;&euro;&brvbar; The N-R method should converge to a root.

### How do you do the square root of 7?

The Newton - Raphson method of successive approximations is easily implemented on a computer. You make a guess, test it by squaring it and compare it with the original target. JCF

### What is the square root of 54?

Approximately 7.34847, rounded to 5dp. The square root of any number can be found through the Newton-Raphson and Secant fixed point iteration methods. See links below for more info.7.3484692

### How do you find the root cube of a number?

If you have a calculator, it is simplicity itself. But if not, there is no simple way. You can use trial-and-improvement, but even that becomes cumbersome when you have a number with three or more non-zero digits. Numerical methods, like Newton-Raphson will also become very difficult.

### What is the approximation for the cube root of 8132?

203 = 8000 Let f(x) = 8132 - x3 then f'(x) = the derivative of f(x) = -3x2 Using Newton-Raphson method, a better estimate is 20 - f(x)/f'(x) = 20 - 132/(-3*202) = 20 + 132/1200 = 20 + 11/100 = 20.11

2 cube root 6

### What is two different ways to calculate the square root of 225?

There are many more than 2 ways:Use a calculator.Learn your tables.Bracket the square root.Use a method which resembles long division.Use the Newton-Raphson (or other numerical) method.