Efficiently Approximate sqrt(35) Using Binomial Series | 10^-7 Accuracy

[sami23]

Use binomial series to approximate sqrt (35) with an accuracy of 10^(-7)

(35) = sqrt(35*36/36) = 6*sqrt(35/36)
Formula: (1+x)^n where x=(-1/36) and n=(1/2):

6*sqrt(35/36) = 6[(1 + (- 1/36))^(1/2)] =

from k=0 to k=4:
= 6[(1 - (1/2)*(1/36) + (1/8)*(1/36)^2 - (1/16)*(1/36)^3 +
(5/128)*(1/36)^4]

= 5.917237472 but it has to be more accurate

I don't know where the mistake is in the series. I used the 4 terms because (5/128)(1/36) = 2.30*10^(-8) Please help, thanks again.

 

[mathman]

The coefficient for the square term should be -1/8, not 1/8. Specifically it is (1/2)(-1/2)/2.

I didn't look any further.