How do you calculate #4sqrt(5)# ?
3 Answers
See below.
Explanation:
If you were to type
I hope that helps!
Explanation:
Explanation:
Note that
So
Note that in general:
#sqrt(a^2+b) = a+b/(2a+b/(2a+b/(2a+b/(2a+...))))#
So we can put
#4sqrt(5) = sqrt(80) = sqrt(9^2-1) = 9-1/(18-1/(18-1/(18-1/(18-...))))#
We can terminate this generalised continued fraction early to get rational approximations to
For example:
#4sqrt(5) ~~ 9-1/18 = 8.9bar(4)#
#4sqrt(5) ~~ 9-1/(18-1/18) = 9-18/323 = 2889/323 ~~ 8.944272#
#4sqrt(5) ~~ 9-1/(18-1/(18-1/18)) = 9-1/(18-18/323) = 9-323/5796 = 51841/5796 ~~ 8.94427191#