Find the smallest whole number that divides 2,925 to make it a perfect square. Then find the perfect square and its square root.

Divide 2,925 by prime numbers.

So, the prime factorization of 2,925 is $3 \times 3 \times 5 \times 5 \times 13 = 3^2 \times 5^2 \times 13$.

For a number to be a perfect square, all its prime factors must appear an even number of times. In the factorization $3^2 \times 5^2 \times 13$, the prime factors 3 and 5 are in pairs, but 13 is not.

To make 2,925 a perfect square, we must divide it by the unpaired prime factor, which is 13.
The smallest whole number to divide by is 13.

Divide 2,925 by 13:

The new perfect square number is 225.

The square root of the new perfect square number is 15.

The smallest whole number to divide by is $\boxed{13}$.
The perfect square number obtained is $\boxed{225}$.
The square root of the perfect square number is $\boxed{15}$.