Question

Explain the steps to find the cube root of 42.5

Answer 1

let x=42.5^(1/3) ,then x^3=42.5 ,(x^3)-42.5=0
now,let f(x)=(x^3)-42.5 ,f '(x)=3x^2
using formula x(n+1)=x(n) - (f[x(n)]/f '[x(n)]) where x(n) is the initial guess value(u can simple substitute a value) and x(n+1) is the better approximation.repeat the process 3 to 4 times u can get the value of cubic root 42.5 qiute accurately.this method is called newton raphson method

Answer 2

one way is write x=42.5^(1/3). cube it
x3=42.5 or x3-42.5=0
use the newton's raphson method to solve it....
f(x)=x3-42.5
df/dx=3x2
so x1=x0-f(x)/f'(x) = x-(x3-42.5)/3x2 = (3x3-x3+42.5)/3x2=(2x3+42.5)/3x2 =1/3(2x+42.5/x2)
take starting x=4 to start with.
obtain the next x from the above relation.
use it to obtain the successive x's...continue till ur satisfied or the x1 and x used are equal

Answer 3

\[c^{a/b} = \sqrt[b]{c^{a}}\]