Formal:
* Sanction: This implies official permission or authorization.
* Endorsement: This suggests a public declaration of support.
* Authorization: This signifies formal permission to proceed.
* Ratification: This implies confirming or formally approving something previously agreed upon.
Informal:
* Okay: This is a casual way to indicate agreement.
* Go-ahead: This suggests permission to proceed.
* Thumbs up: This is a gesture indicating approval.
* A-okay: This is a colloquial expression meaning "all right" or "approved."
* Green light: This refers to the permission to begin something.
Other:
* Consent: This implies willing agreement.
* Acceptance: This signifies taking something as satisfactory.
* Commendation: This implies praise or recognition.
* Favorable: This suggests a positive opinion.
The best synonym for approval depends on the specific context and desired nuance.