$n=\sqrt{\epsilon \mu }$
Negative refractive index happens when permittivity ($\epsilon $) and permeability ($\mu $)of a material is negative. My question is, if permittivity and permeabilitity of a material is negative then the end product, according to the above equation, should be positive. If two negative numbers multiplied should give a positive number. Then why in here two negative numbers ($\epsilon $ and $\mu $) gives a negative refractive index?