Following up from my previous post (Power series expansion of (1-x)^-1/2. Approximating the value of square root 2.), this is the real deal. The question is; "Use a power series expansion to approximate Square Root 3. Comment on the reasonableness of your result." Disclaimer: we have been taught nothing on Power series, Taylor series or binomial series. After doing 2 hours of research online, I find myself still confused. I understand how they expand now because of these articles https://en.wikipedia.org/wiki/Taylor...eral_variables , https://en.wikipedia.org/wiki/Binomial_theorem.

I can't understand how they work to approximate square root values. Look at this and open the answer for Example 5b: 4. The Binomial Theorem .It's a procedure for approximating the value of a cube root and it looks like it worked (ofc, they used an expansion for cube root). I thought I understood it then but I tried it for the expansion of square root 3. Applying the same method; so after working out the expansion and then substituting x for 2, it just didn't work. No where near the answer.

Really stuck here. Any help is appreciated, even if you can improve my understanding of these power series expansions being used for approximation.