AHSME 1961 Problem 4

Let the set consisting of the squares of the positive integers be called $u$; thus $u$ is the set $1, 4, 9, 16 \ldots$. If a certain operation on one or more members of the set always yields a member of the set, we say that the set is closed under that operation. Then $u$ is closed under: $\textbf{(A)}\ \text{Addition} \textbf{(B)}\ \text{Multiplication} \textbf{(C)}\ \text{Division} \\ \textbf{(D)}\ \text{Extraction of a positive integral root} \textbf{(E)}\ \text{None of these}$