A is the smallest number such that both 1452 × A and 1452 ÷ A are complete…

The prime factorization of 1452 is $2^2 \times 3^1 \times 11^2$. For the product $1452 \times A$ to be a perfect square, all prime exponents must be even. Since the exponent of 3 is odd (1), A must include a factor of 3 to make it even. For the quotient $1452 \div A$ to be a perfect square, A must divide 1452 and eliminate the odd exponent of 3. The smallest integer satisfying both conditions is A = 3.