Finding root-mean-square speed of neon using kinetic energy
As hinted in the comments by @AngusTheMan we use the equation
$$\mathrm{KE_{avg}} = \frac{3}{2}kT,$$
but ultimately we are looking for the $v_\mathrm{rms}$, so we'll also use
$$v_\mathrm{rms} = \sqrt{\frac{3RT}{M}}.$$
You've been given your $\mathrm{KE_{avg}},$ $R$ and $k$ are constants, and $M$ is the mass of 1 mole of $\ce{Ne}$. We can set all of these equal and the solution will come from
$$v_\mathrm{rms} = \sqrt{\frac{3 \cdot R\cdot\mathrm{KE_{avg}}\cdot\frac{2}{3k}}{M}}.$$