  We show that for every $\Delta\in\mathbb N$, there exists a constant $C$ such
that if $G$ is an $(n,d,\lambda)$-graph with $d/\lambda\ge C$ and $d$ is large
enough, then $G^2$ contains every $n$-vertex tree with maximum degree bounded
by $\Delta$. This answers a question of Krivelevich.
