To multiply the square root of 3 cubed by the square root of 9 cubed, we can start by simplifying each term individually.
First, let's find the cube of 9. It means multiplying 9 by itself twice: 9 * 9 * 9 = 729. So you are correct that 9 cubed is equal to 729.
Next, let's find the cube of 3. Again, it means multiplying 3 by itself twice: 3 * 3 * 3 = 27. So 3 cubed is equal to 27.
Now that we have simplified the terms, we can multiply them together: sqrt(27) * sqrt(729).
This can be simplified as follows:
sqrt(27) = sqrt(9 * 3) = sqrt(9) * sqrt(3) = 3 * sqrt(3).
Similarly,
sqrt(729) = sqrt(9 * 81) = sqrt(9) * sqrt(81) = 3 * 9.
Now we can multiply the simplified terms:
(3 * sqrt(3)) * (3 * 9) = 9 * 3 * 3 * 9 = 729.
Therefore, the answer is 729, which is a whole number.