Answer
$ 1.00429$
Work Step by Step
We know that the rms speed is given by
$$v_{\rm rms}=\sqrt{\dfrac{3k_BT}{m}}$$
Hence the ratio of the rms speed of $\rm ^{235}UF_6$ to that of $\rm ^{238}UF_6$ is
$$\dfrac{(v_{\rm rms})_{\rm ^{235}UF_6}}{(v_{\rm rms})_{\rm ^{238}UF_6}}=\sqrt{\dfrac{m_{\left(\rm ^{\bf 238}\;UF_6\right)}}{m_{\left(\rm ^{\bf235}\;UF_6\right)}}}$$
we canceled the identical variables $3k_BT$
where $m$ is the atomic mass of the element,
Plugging the known;
$$\dfrac{(v_{\rm rms})_{\rm ^{235}UF_6}}{(v_{\rm rms})_{\rm ^{238}UF_6}}=\sqrt{\dfrac{M_{\rm U^{238}}+M_{\rm F} }{ M_{\rm U^{235}}+M_{\rm F}}}$$
$$\dfrac{(v_{\rm rms})_{\rm ^{235}UF_6}}{(v_{\rm rms})_{\rm ^{238}UF_6}}=\sqrt{\dfrac{(238)+(6)(19) }{ (235)+(6)(19) }}=\color {red}{\bf 1.00429}$$
