Do you have to pay royalties play music like Mozart or Beethoven on the radio?

In most cases, no. Music by composers who have been dead for more than 50 years are considered public domain and may be performed or broadcast without paying royalties. However, some exceptions may apply, such as if a particular arrangement of the music is still under copyright. It's always best to check with a music licensing expert or the composer's estate to confirm the copyright status of a particular work.