No, 2352 is not a perfect square.
To find the smallest number by which 2352 must be multiplied so that the product is a perfect square, we need to factorize 2352 into its prime factors.
2352 = 2^4 x 3 x 7^2
To make it a perfect square, we need to multiply it by 2^2 and 7, which gives us:
2352 x 2^2 x 7 = 9408
Now, we can take the square root of 9408:
√9408 = √(2^8 x 3 x 7) = 2^4 x √(3 x 7) = 16√21
Therefore, the smallest number by which 2352 must be multiplied so that the product is a perfect square is 2^2 x 7, which gives us the square root of 9408 as 16√21.