# 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)]#