The correct response is:
At least one factor is irrational because the product is irrational.
Since the product is \( \sqrt{225} \), which simplifies to 15 (a rational number), it indicates that there can be two factors: both could be rational, or one could be rational and the other irrational. However, since we know 15 is rational, we cannot conclude that either factor must be irrational without additional information. Therefore, the earlier statement referencing irrationality was inaccurate in this context.
In essence, both factors can be rational, especially since the square root of 225 gives a rational product. Thus, the response "They are both rational because the product is rational" would be more appropriate regarding rationality. The given confusion arises from considering \( \sqrt{225} \) itself and not a multiplication of factors producing that product.