The result of the expression $3\sqrt{9} - 4\sqrt[3]{64}$ is $-7$.

Would you like more details or have any questions about the steps involved?

Here are 5 related questions to explore further:

1. What is the difference between square roots and cube roots?
2. How do you simplify expressions involving roots?
3. How do you solve equations with both square and cube roots?
4. What are some real-world applications of roots in equations?
5. Can cube roots be negative, and how would that change the calculation?

Tip: When working with roots, always check if the number under the root sign is a perfect square or cube to simplify your calculations.