The translation su agrees in number with the noun which it modifies; their is translated by su, sus, depending on what follows: their father/mother su padre/madre; their books/magazines sus libros/revistas. For their used with parts of the body,
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The RAE (Real Academia de la Lengua Española) is a body established in the eighteenth century to record and preserve the Spanish language. It is made up of académicos, who are normally well-known literary figures and/or academic experts on the Spanish language. The RAE publishes the Diccionario de la Real Academia Española, which is regarded as an authority on correct Spanish. Affiliated academies exist in Latin American countries.