The significant law in the United States that abolished the racist practices of segregation in public places is the Civil Rights Act of 1964. This landmark legislation prohibited discrimination based on race, color, religion, sex, or national origin. It aimed to eliminate barriers to voting, ensure equal access to public accommodations, and strengthen enforcement against discriminatory practices. The passage of the Civil Rights Act was a pivotal moment in the American civil rights movement, empowering activists and laying the groundwork for future legal advancements in social justice and equality, furthering the cause of civil rights.