How do we know the righteousness of God is through faith?

Romans 3:21-22 explains that the righteousness of God is manifested apart from the law, being witnessed by the law and the prophets. It is through faith in Jesus Christ that this righteousness is applied to all who believe. This illustrates that our human attempts at righteousness through the law ultimately fail and that the true righteousness that God accepts is found through faith in Christ alone. This is reinforced by Galatians 2:16, which states that we are justified not by works of the law, but by the faith of Christ.