Answer
$\frac{v_{238}}{v_{235}}=0.996$
Work Step by Step
We can find the ratio of the rms speeds of the two isotopes as follows:
We know that the rms speed is given as
$v_{rms}=\sqrt{\frac{3RT}{M}}$
Now $\frac{v_{rms,238}}{v_{rms,235}}=\frac{\sqrt{\frac{3RT}{M_{238}}}}{\sqrt{\frac{3RT}{M_{235}}}}$
$\frac{v_{rms,238}}{v_{rms,235}}=\sqrt{\frac{M_{235}}{M_{238}}}$
We plug in the known values to obtain:
$\frac{v_{rms,238}}{v_{rms,235}}=\sqrt{\frac{349}{352}}=0.996$
