NMC 1990 Problem 2

Let $a_{1}, a_{2}, \ldots, a_{n}$ be real numbers. Prove

$$\sqrt[3]{a_{1}^{3}+a_{2}^{3}+\ldots+a_{n}^{3}} \leq \sqrt{a_{1}^{2}+a_{2}^{2}+\ldots+a_{n}^{2}}$$

When does equality hold in (1)?