Theta bound of the following function
First, note that  we print a * for every tuple $(i,j,k,r)$ such that
$0 \leq  i \leq j \leq k-200 \leq \sqrt{r}-200\leq \sqrt{n}-200$ 

For every $i$ and $j$ there are at most $(\sqrt{n}-200)$ options, for $k$ it is $\sqrt{n}$ and for $r$ it is $n$. Thus the upper bound for the number of * is $(\sqrt{n}-200)\cdot (\sqrt{n}-200) \cdot \sqrt{n} \cdot  n\in O(n^{2.5})$.

To compute the lower bound, we can take $i$'s in the range between $0$ and $\frac{\sqrt{0.5n}-200}{2}$, $j's$  between $\frac{\sqrt{0.5n}-200}{2}+1$ and $\sqrt{0.5n}$, $k$'s between $\sqrt{0.5n}+1$ and $\sqrt{0.75n}$, and finally, $r's$ between $0.75n+1$ to $n$. Thus the number of options for a tuple $(i,j,k,r)$ is more than $(\frac{\sqrt{0.5n}-200}{2})^2 \cdot (\sqrt{0.75n}-\sqrt{0.5n})\cdot 0.25n \in \Omega(n^{2.5})$.

Thus the answer is $\Theta(n^{2.5})$