Can you proceed?
Need a little hint on this one.
Expand in ascending powers of as far as the term in , simplifying the terms as much as possible. By substituting 0.08 for in your result obtain an approximate value of the cube root of 5, upto four decimal places.
I expanded the problem as a binomial series,
The rest of the question is confusing me. How do I break up 5 to include 0.08?
The only approach I could think of was,
Then using x = -3/8, to put in the above equation.
This gives me 1.7122 which is incorrect, and also does not use the suggested 0.08. Any ideas where I am going wrong?
Thanks for your help.
Thanks! That's exactly what I was looking for. Didn't make the connection with the fractional indices. Fits nicely!
One more question if you don't mind. The method I choose is clearly inaccurate but using 0.08 and your suggestion gives a much more accurate answer. How would you approach this problem if 0.08 was not provided and you were asked to find the cube root? I mean the 0.08 is the key but what train of thought would get you to make this assumption?