To verify a radical equation algebraically, one must isolate the radical on one side and then square both sides to eliminate the radical. After squaring, it is essential to simplify the equation and check for extraneous solutions by substituting back into the original equation. The discussion emphasizes the importance of ensuring both sides of the equation are equal after manipulation. Additionally, referencing previous questions on the topic can provide valuable insights and methods for solving similar problems. This approach ensures a thorough understanding of radical equations and their verification.