$n=\sqrt{\epsilon \mu }$

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

$n=\sqrt{\epsilon \mu }$

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?

$n=\sqrt{\epsilon \mu }$

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

$n=\sqrt{\epsilon \mu }$

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