The visible ending yāʾ in رَضِيَ is not proof that the root ends in yāʾ. Its root is ر ض و, and the perfect undergoes wāw-to-yāʾ substitution.
Word / formMeaning / explanation
رَضِيَfinal moving yāʾ in the perfect.
يَرْضَىalif maqṣūrah in the imperfect.
رَاضٍindefinite active participle.
مَرْضِيٌّgeminated yāʾ in the passive participle.
These are different derived shapes of one root; a new surface ending does not necessarily mean a new lexical root.