# What is the square root of 337?

##### 1 Answer

#### Explanation:

As a result,

It is an irrational number which when squared (multiplied by itself) gives you

Since it is irrational, its decimal representation neither terminates nor recurs.

It has a continued fraction expansion which does repeat, namely:

#sqrt(337) = [18;bar(2,1,3,1,11,2,4,1,3,3,1,4,2,11,1,3,1,2,36)]#

#=18+1/(2+1/(1+1/(3+1/(1+1/(11+1/(2+1/(4+1/(1+...))))))))#

To construct rational approximations for

For example:

#sqrt(337) ~~ [18;2,1,3,1] = 18+1/(2+1/(1+1/(3+1/1))) = 257/14 ~~ 18.357#