calculus - The limit of general term in a series

I have the following statement -

If $\sum_{1}^{\infty} a_{n}^2$ converge then $\sum_{1}^{\infty} a_{n}^3$ converge.

Well i know this statement is true , but if can someone explain why

$\lim_{n\rightarrow\infty}(a_{n}^2) = 0$ implies that $\lim_{n\rightarrow\infty}(a_{n}) = 0$

(a fact that help to prove this statement) , Thanks!