I'm completely stuck on the question, Find the square root of 51 correct to 4dp using binomail series. Ive attempted this but clearly made a serious error somewhere because the numbers get very large indeed.
Any help would be great
$\displaystyle \sqrt{51} = \sqrt{49+2} = 7\sqrt{1+(2/49)}$. Use the binomial expansion of $\displaystyle (1+x)^{1/2}$ with x = 2/49. The terms will get small quite rapidly, so you should not need very many to get within 4dp accuracy. (Don't forget to multiply by 7 at the end to get the correct answer.)