Does the dielectric constant and relative permeability of a medium relate to its refractive index?

I know that in a vacuum,

$$c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}.$$

Does this apply to any medium, so that

$$c=\frac{1}{\sqrt{\varepsilon\mu}},$$

and its index of refraction is related to its dielectric constant and relative permeability by

$$n=\sqrt{\kappa\mu_r}.$$

I tried this for water, which has a dielectric constant of about $$80$$ and a relative permittivity of about $$1$$, but then the index of refraction is about $$8.9$$ when its actually $$1.33$$. Where did I go wrong in my assumptions/calculations?