Radical Expression Simplification: Worked Example and Explanation

This document provides a complete and clear step-by-step explanation of how to simplify the radical expression: √192 − 3√50 + 2√98 − 2√108 It is designed to help students understand how to break down square roots, identify the largest square factors, and combine like radical terms. Each step is fully explained so learners can follow the logic and method behind the simplification process. What This Document Covers: How to express each radical in the form a√b How to find the greatest square factor of a number How to simplify radicals such as √192, √50, √98, and √108 How to multiply coefficients with square roots How to combine like terms (√2 with √2, √3 with √3) A clear final simplified answer Key Learning Points: √192 becomes 8√3 3√50 becomes 15√2 2√98 becomes 14√2 2√108 becomes 12√3 Like radicals are grouped and simplified: (8√3 − 12√3) = −4√3 (−15√2 + 14√2) = −√2 Final Simplified Expression: −4√3 − √2 Why This Document Is Useful: Ideal for students learning algebra or radical expressions. Helpful for homework, assignments, and test preparation. Easy-to-follow breakdown suitable for beginners and intermediate learners. Provides structured reasoning rather than only the final answer.