9. Calculate (without using a calculator) $\sqrt[3]{9+4 \sqrt{5}}+\sqrt[3]{9-4 \sqrt{5}}$, given that this number is an integer.
Answer: 3.

Solution: Note that $2<\sqrt[3]{9+4 \sqrt{5}}<3$ and $0<\sqrt[3]{9-4 \sqrt{5}}<1$. Therefore, $2<\sqrt[3]{9+4 \sqrt{5}}+\sqrt[3]{9-4 \sqrt{5}}<4$, hence this number is 3.