"Root on" is a phrasal verb which means to encourage or support someone, especially during a competition or challenge. Some synonyms for "root on" include cheer, motivate, inspire, spur, urge, and rally. These words all convey the idea of providing someone with the necessary support and motivation to achieve success. Additionally, other synonyms such as back, encourage, applaud, and praise can also be used to convey similar meanings. It's important to use synonyms effectively to add variety and nuance to written or spoken communications, and to tailor the message to the specific context or audience.