The cube root of 729 is:

$\sqrt[3]{729} = 9$

Explanation: Since $9^3 = 9 \times 9 \times 9 = 729$, the cube root of 729 is 9.

Would you like more details or have any questions on cube roots?

Here are some related questions:

1. How do you calculate the cube root of other numbers?
2. What is the cube root of negative numbers?
3. How do you solve equations involving cube roots?
4. What is the difference between square roots and cube roots?
5. How can cube roots be applied in real-life scenarios?

Tip: The cube root of a number $x$ is the value that, when multiplied by itself three times, equals $x$.