How do you find the square root of 17?
1 Answer
Jun 26, 2016
We can calculate rational approximations like:
#sqrt(17) ~~ 268/65 ~~ 4.1231#
Explanation:
Since
It is an irrational number a little larger than
Since
#sqrt(17) = [4;bar(8)] = 4+1/(8+1/(8+1/(8+1/(8+1/(8+1/(8+...))))))#
You can terminate this continued fraction expansion early to get rational approximations to
For example:
#sqrt(17) ~~ [4;8,8] = 4+1/(8+1/8) = 4+8/65 = 268/65 = 4.1bar(230769)#
Actually:
#sqrt(17) ~~ 4.12310562561766054982#