What is the meaning of check out?

verb

• Examine so as to determine accuracy, quality, or condition.
  • usage: "check the brakes"; "Check out the engine"
  • synonyms: check, check up on, look into, suss out, check over, go over, check into
• Announce one's departure from a hotel.
• Be verified or confirmed; pass inspection.
  • usage: "These stories don't check"
  • synonyms: check
• Trace.
  • usage: "We are running down a few tips"
  • synonyms: run down
• Record, add up, and receive payment for items purchased.
  • usage: "She was checking out the apples that the customer had put on the conveyer belt"
• Withdraw money by writing a check.
  • synonyms: cheque
• Try to learn someone's opinions and intentions.
  • usage: "I have to sound out the new professor"
  • synonyms: sound out, feel out