Racism will exist in this world even when the whole world is educated. It is a product of prejudice, and every human being has prejudiced views which every one will agree about. If someone denies having prejudice views, it highlights his lack of self-consciousness. Historically, racism against the blacks in US was created to exploit them. Racism is a product of black exploitation, not its cause.
The nature of exploitation might have changed in modern US, and it might be visibly perceptible to white Americans, yet colour like brown, black skin prejudice exists in the minds of whites. Still there is conscious and unconscious denial of racism among the whites and therefore the efforts to remove racism completely is almost impossible.
