**Solution:**

To find the number of zeros in the square of 60, we need to determine the number of factors of 10 in the square.

The square of a number can be expressed as the product of the number with itself, i.e., n^2 = n * n.

In this case, we need to find the square of 60.

**Step 1: Breaking down 60 into its prime factorization**

To find the prime factorization of 60, we divide it by prime numbers starting from 2.

60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5

So, the prime factorization of 60 is 2 * 2 * 3 * 5.

**Step 2: Determining the number of factors of 10 in the prime factorization of 60^2**

To determine the number of factors of 10 (2 * 5) in the prime factorization of 60^2, we need to count the number of 2s and 5s.

In the prime factorization of 60^2, we have two 2s and one 5.

Therefore, the number of zeros in the square of 60 is equal to the minimum count of 2s and 5s, which is one.

Hence, the correct answer is option B: 2.

**Explanation:**

In the prime factorization of 60^2, we have two 2s and one 5. The number of zeros in the square of 60 is determined by the minimum count of 2s and 5s, which is one. Since there is one 5 in the prime factorization, we will have one zero in the square of 60. Therefore, the correct answer is option B: 2.