# MATLAB: Finding the 5th Root using Newton's Method

1. May 26, 2012

### pags920

1. The problem statement, all variables and given/known data
The solution of the nonlinear equation x^5-P=0 gives the fifth root of the number
P. A numerical solution of the equation can be calculated with Newton’s
method. The solution process starts by choosing a value x1 as a first estimate of
the solution. Using this value, a second, more accurate solution x2 can be calculated
with x2=x1-((x1^5-P)/(5*x1^4)) , which is then used for calculating a third, still more
accurate solution x3, and so on. The general equation for calculating the value of
the solution xi+1 from the solution x1 is xi+1 = xi -((xi^5-P)/(5*xi^4)) . Write a userdefined
function that calculates the fifth root of a number. For function name and
arguments use y=fifthroot(P), where the input argument P is the number
whose fifth root is to be determined, and the output argument y is the value (5th sqrt(P)) .
In the program use x=P for the first estimate of the solution. Then, by using the
general equation in a loop, calculate new, more accurate solutions. Stop the looping
when the estimated relative error E defined by is smaller than
0.00001.

2. Relevant equations

3. The attempt at a solution

Code (Text):
function [y] = fifthroot(P)
format short
x=P;
xi=1;
i=5;
while n==1:i
xi=xi-((xi^5-P)/(5*xi)^4);
E=abs((xi-x)/x);
if E<0.00001
break
end
disp(x)
end
This was my previous attempt. I am not sure whether a for loop or a while loop is the best to use for this situation. My problem is trying to use a previous answer in computing the next answer. Not quite sure how to retain a previous answer for using in the next one.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 26, 2012

### RoshanBBQ

Your code doesn't even compile. What in the world does while n == 1:i mean? You should instead put the E term in the while statement alongside the 'break' condition. Here is a nice skeleton code I have written

Code (Text):

% Define parameters
endCondition = 0.00001;

E = inf; % Initialize such that while loop begins
while E > endCondition
% code to compute new estimate
% Update E (for use in the while loop compare)
end

Last edited: May 26, 2012
3. Apr 4, 2014

### chem212

i have tried to apply what the both of you said but it is not working for me. Here is what i did. Please let me know what i did wrong.
function [y]= fifthroot (P)
x=p
xi=1
i=5
endcondition=0.00001;
xi=xi-((xi^5-P)/(5*xi)^4);
E=abs((xi-x)/x);
if E<0.00001
break
while E > endcondition %compute new estimate
update E (for use in the while loop compare)
end
end
disp (x)
end
i would really appreciate it