How do you simplify #sqrt(442)#?
1 Answer
Nov 7, 2015
#sqrt(442) = [21;bar(42)] = 21 + 1/(42+1/(42+1/(42+...)))#
Explanation:
It is an irrational number, so it cannot be expressed in the form
However, it is of the form
As a result, the continued fraction for its square root takes a particularly simple form:
#sqrt(442) = [21;bar(42)] = 21 + 1/(42+1/(42+1/(42+...)))#
In general, any positive integer of the form
#sqrt(n^2+1) = [n;bar(2n)]#