# Calculation using Taylor expansion at given point

everyone!

I couldn't really find even a bit of information regarding the type of problem I have. Problem states that I should use Taylor series (expansion) to calculate the given value with error maximum of 0,01.

$$^5\sqrt(250)$$

My mentor gave me a little hint that I should somehow use Binomial Expansion and and take 243 as the nearest fifth root or something like that.

Looking forward to any help, thanks in advance

• Did you expand $(243+7)^{1/5}$ using the general binomial expansion of $(x+y)^r$? It will give you an alternating series which will allow you to determine how many terms you must sum to obtain the accuracy required. – John Wayland Bales Mar 16 '17 at 19:28
• Thank you a lot! That helped – Aidar Nugmanov Mar 16 '17 at 19:55

The value of the third term is $0.0002$ which means that the sum of the first two terms will give an accuracy $\pm0.0002$ which will satisfy the accuracy requirements.
So the answer is the sum of the first two terms, $3.02$ although you get a better answer if you use the three decimal place answer of $3.017$.
• In that case you would have to expand $(1024-774)^{1/5}$ which would take many more terms to obtain the required precision. Also that series would not alternate. – John Wayland Bales Mar 16 '17 at 19:58