Two transparent media, A and B , have relative permittivities _A...

The speed of light $v$ in a material medium is given by the relation:
$v = \dfrac{c}{\sqrt{\mu_r \epsilon_r}}$
where $c$ is the speed of light in vacuum, $\mu_r$ is the relative permeability, and $\epsilon_r$ is the relative permittivity of the medium.

For medium $A$, $v_A = \dfrac{c}{\sqrt{\mu_A \epsilon_A}}$

For medium $B$, $v_B = \dfrac{c}{\sqrt{\mu_B \epsilon_B}}$

Taking the ratio of the two speeds:
$\dfrac{v_A}{v_B} = \dfrac{\dfrac{c}{\sqrt{\mu_A \epsilon_A}}}{\dfrac{c}{\sqrt{\mu_B \epsilon_B}}} = \sqrt{\dfrac{\mu_B \epsilon_B}{\mu_A \epsilon_A}}$

Answer: $\sqrt{\dfrac{\mu_B \epsilon_B}{\mu_A \epsilon_A}}$