Show that $ {W_t} = \sum\limits_{i \geqslant 1} {{1_{\left\{ {\sqrt {{T_i}} \leqslant t} \right\}}}} $ is a Poisson process

Question

Let $N_t$ be a homogeneous Poisson process with intensity $1$.

$T_i$ the arrival times of $N_t$

Let $\sqrt {{T_i}}$ the arrival times of a point process $W_t$

Show that $W_t$ is a Poisson process