smc

Consider each option, case by case. For option A, note that $1+4=5$, so the set is not closed under addition because $5$ is not a perfect square. For option B, note that $9\cdot 4=36$ and $4\cdot 25=100$. Letting one member of the set be $a^2$ and another member be $b^2$ (where $a$ and $b$ are positive integers), the product of the two members is $(ab{)}^2$. Since $ab$ is an integer and $(ab{)}^2$ is a perfect square, the set is closed under multiplication. For option C, note that $9÷4=2.25$, so the set is not closed under division because $2.25$ is not an integer. For option D, note that $\sqrt{4}=2$, so the set is not closed under extraction of a positive integral root because $2$ is not a perfect square. Thus, the answer is $\boxed{\text{Multiplication}}$.