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Quick Answer.  Noble gases are unreactive because their outer electron shells are full and therefore in their most stable state. Normally, elements react with one another because they have incomplete electron shells. They lose, gain or share electrons in order to gain a more stable electron configuration.
An inert gas is any gas that is not reactive with elements. Like the noble gases an inert gas is not necessarily elemental and are often compound gases. Like the noble gases the tendency for non-reactivity is due to the valence, the outermost electron shell, being complete in all the inert gases.