The smallest number by which 588 must be divided so that the product is a perfect square?

To find the smallest number by which 588 must be divided so that the product is a perfect square, follow these steps:

1. First, factorize the number 588. The prime factors of 588 are 2, 2, 3, and 7*7.

2. To make 588 a perfect square, each prime factor must appear an even number of times. In the prime factorization of 588, 2 appears twice, 3 appears once, and 7 appears twice.

3. The number 3 appears only once, which is odd. Therefore, 588 must be divided by 3 to make it a perfect square.

So, the smallest number by which 588 must be divided to make it a perfect square is 3.