This uses a charade (parts joined together) combined with a homophone. A charade links separate word parts to form the answer, while a homophone uses a word that sounds like another word.
Take the first part of 'resolution' (3 letters), then add a homophone indicated by 'on the radio' - you need a word that sounds like what you use to 'check out' or examine things.
Answer: RESIZE | RES (first part of 'resolution') + IZE (sounds like 'eyes', which check out/examine things, indicated by 'on the radio' for the homophone)