Used to suggest that an action, though not guaranteed to succeed, is likely useful enough to try.
“It might be worth checking if the warranty still covers the repair.”
“It might be worth asking for a second opinion before we sign the contract.”
This cautious, hedging phrase is common when a speaker offers a suggestion without being fully certain it will solve the problem. In Listening Part 1, this kind of tentative language can hint that the idea is only partially adopted, so listen for the other speaker's reaction to judge whether it's accepted.
Synonyms: it could be worthwhile to, it may pay to, it's probably worth