What is the 200th term of the increasing sequence of positive integers formed by omitting only the perfect squares?
When 200 is reached in the sequence of non-square positive integers, all the perfect squares from $1^2$ up to $14^2$ have been omitted.  Therefore, 200 is the 186th term.  The 187th term is 201, the 188th term is 202, $\ldots$, the 200th term is $\boxed{214}$.