How to Simplify Square and Cube Roots

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step guide on how to simplify square roots, moving beyond basic perfect squares to more complex, non-perfect numbers. Hosted by a narrator named Justin, the lesson begins by reviewing the inverse relationship between squaring and square roots using familiar perfect squares like 49 and 36. It then introduces the core technique for simplifying non-perfect squares: prime factorization. The video demonstrates how to break numbers down into their prime factors, identify pairs, and "pull them out" of the radical to create a simplified expression. The content covers key algebraic themes including prime factorization, the properties of radicals, and the distinction between rational and irrational numbers. It provides detailed walkthroughs of three specific examples: the square root of 216, the square root of 810, and an extension problem involving the cube root of 250. Through these examples, the video establishes a consistent algorithm: factor the number inside the radical, group identical factors (pairs for square roots, triplets for cube roots), move one representative from each group outside the radical, and multiply the remaining terms. For educators, this video serves as an excellent instructional tool for Algebra I or Pre-Algebra classes. It demystifies a procedural skill that often confuses students by providing a visual and logical method (the pairing strategy) rather than just rote memorization. The clear visual layout, where factors are grouped and moved explicitly, helps students visualize the mathematical operations. It is particularly useful for introducing the concept of exact form versus decimal approximation and prepares students for future topics involving radical operations and variables.