Explanation:
When two dice are thrown simultaneously, the total number of outcomes is 36 (since each die has 6 faces and there are 6 x 6 = 36 possible combinations).

To find the probability that the product of the numbers appearing on the top faces of the dice is a perfect square, we need to determine the favorable outcomes.

Favorable Outcomes:
The product of two numbers is a perfect square if and only if each of the numbers itself is a perfect square.

There are 6 perfect squares between 1 and 6, namely 1, 4, 9, 16, 25, and 36.

Therefore, the favorable outcomes are the combinations in which both numbers are perfect squares. These combinations are:
(1, 1), (4, 4), (9, 9), (16, 16), (25, 25), (36, 36)

There are 6 favorable outcomes.

Probability:
The probability of an event is given by the ratio of favorable outcomes to the total number of outcomes.

Therefore, the probability that the product of the numbers appearing on the top faces of the dice is a perfect square is:
Probability = (Number of favorable outcomes) / (Total number of outcomes) = 6 / 36 = 1 / 6

Hence, the correct answer is option B) 1/6.

Alternative Approach:
We can also solve this problem using the concept of counting the favorable outcomes directly.

We have 6 possible outcomes for each die, so the total number of outcomes is 6 x 6 = 36.

The favorable outcomes are:
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

There are 6 favorable outcomes.

Therefore, the probability of the product being a perfect square is:
Probability = (Number of favorable outcomes) / (Total number of outcomes) = 6 / 36 = 1 / 6

Again, the correct answer is option B) 1/6.

Conclusion:
The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is 1/6 or 2/9. Thus, the correct answer is option B) 2/9.