The squarefree part of a monomial $x^\textbf{u}$ is $\prod_{i:u_i>0}x_i$. Show that if $\textit{I} = \langle{x^{\textbf{u}_1}, ..., x^{\textbf{u}_r}}\rangle$ is a monomial ideal, then the radical $\sqrt{I}$ is generated by the squarefree parts of $x^{\textbf{u}_1}, ..., x^{\textbf{u}_r}$.
It is a bit different than defining that an ideal generated by squarefree monomials is indeed a radical ideal, but I don't really know how to tacke it this way.