1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Binomial series - Finding square root of number problem

  1. Apr 27, 2014 #1
    1. The problem statement, all variables and given/known data

    Expand ##(1+x)^(1/3)## in ascending powers of x as far as the term ##x^3##, simplifying the terms as much as possible. By substituting 0.08 for x in your result, obtain an approximate value of the cube root of 5, giving your answer to four places of decimals.


    2. Relevant equations

    Binomial series.

    3. The attempt at a solution
    Expansion as per binomial series :
    ##1+(1/3)x - (1/9)x^2 + (5/81)x^3##.

    No idea how to find cube root of 5 by using x = 0.08.
    Help please!
    Sorry if I am asking too many questions - I don't have a tutor for this, I'm on my own

    Thanks! :)
     
  2. jcsd
  3. Apr 27, 2014 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Are you sure you have read the problem correctly? Putting x= 0.08 into that formula will give you [itex](0.08+ 1)^{1/3}= 1.08^{1/3}[/itex], not [itex]\sqrt[3]{5}[/itex]. 5= 4+ 1 so you should set x= 4 to use that formula to find [itex]\sqrt[3]{5}[/itex].
     
  4. Apr 27, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    [
    That would approximate ##\sqrt[3]{5}## by a few terms of a divergent series, which does not look like a good idea. However, using ##2^3 = 8## we can write
    [tex] 5 = 8 - 3 = 8 \left(1 - \frac{3}{8}\right) \Longrightarrow 5^{1/3} = 2 (1 - 0.375)^{1/3}[/tex]

    BTW: please try not to confuse everybody by using a bad thread title. Don't say "square root" when you mean "cube root".
     
    Last edited: Apr 27, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Binomial series - Finding square root of number problem
Loading...