What's the square root of 146?
1 Answer
Aug 10, 2018
Explanation:
Note that
Being of the form
[n;bar(n,2n)] = n+1/(n+1/(2n+1/(n+1/(2n+1/(n+1/(2n+...))))))
which since the continued fraction does not terminate, is irrational.
So:
sqrt(146) = [12,bar(12,24)]
color(white)(sqrt(146)) = 12+1/(12+1/(24+1/(12+1/(24+1/(12+1/(24+...))))))
color(white)(sqrt(146)) ~~ 12+1/(12+1/(24+1/12)) = 42049/3480