Calculate Any Square Root by Hand - Actual Harvard Entrance Exam

Learn the traditional square root algorithm used in MIT and Harvard entrance exams from the 1800s to calculate the square root of any number by hand without a calculator. Master this digit-by-digit method through step-by-step examples including whole numbers like 2025, 831744, and 13689, as well as decimal numbers such as 11.56 and 531.5. Discover the historical context of this mathematical technique, exploring its origins with ancient mathematician Aryabhata and understanding why the algorithm works through mathematical principles. Practice calculating square roots manually using the same methods that were once required knowledge for admission to prestigious universities, complete with explanations of place value concepts and the underlying mathematical reasoning behind each step of the process.