  Grosu [On the algebraic and topological structure of the set of Tur\'{a}n
densities. \emph{J. Combin. Theory Ser. B} \textbf{118} (2016) 137--185] asked
if there exist an integer $r\ge 3$ and a finite family of $r$-graphs whose
Tur\'{a}n density, as a real number, has (algebraic) degree greater than~$r-1$.
In this note we show that, for all integers $r\ge 3$ and $d$, there exists a
finite family of $r$-graphs whose Tur\'{a}n density has degree at least~$d$,
thus answering Grosu's question in a strong form.
