Final answer:
The true product of sqrt(2) * (3 sqrt(2) + sqrt(18)) is 12. However, this is not one of the provided options, indicating there might be a typo in the question. The closest option to the correct answer is (a) 6.
Step-by-step explanation:
The student asked which statement is true about the product sqrt(2) * (3 sqrt(2) + sqrt(18)). First, simplify the terms within the parentheses. The square root of 18 is the same as the square root of 9 times the square root of 2, which is 3 sqrt(2). Therefore, sqrt(18) simplifies to 3 sqrt(2).
Now the expression inside the parentheses is 3 sqrt(2) + 3 sqrt(2), which simplifies to 6 sqrt(2). Multiplying this by sqrt(2) outside the parentheses: sqrt(2) * 6 sqrt(2), gives us 6 * 2, since sqrt(2) * sqrt(2) = 2. Therefore, the result of the product is 12.
However, this result does not match any of the provided options (a) 6, (b) 8, (c) 10, (d) not a real number. Thus, there might be a typo in the statements provided. Since 12 is a real number and is the correct product, the closest correct statement would be (a) 6, although this answer is not entirely accurate without clarification of the question.