I would use 'radical' to refer to two situations. 'Radical' could describe an extreme difference between two things. "His new album is a radical departure from his earlier work." "China's economy experienced a radical change under Deng Xiao Peng." 'Radical' can also be used to describe some political, economic or social belief that is lacking in moderation. "His belief in polygamy was radical." "His scientific theories were considered radical at the time." 'Radical' can also mean basic, something at the root, but it is seldom used in this way in normal conversation.