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Four numbers are chosen from the set $3$, $6$, $12$, $27$, $48$ so that the product is a perfect square. What is the number that was not chosen? 
Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers
Obsever that $3\times27=9^{2}$ and $12\times27=24^{2}$ are both squares. Hence, their product is also a perfect square and the fifth number must be $6$. 