Do Not Square Both Sides! Do This Instead.

In this video, we solve the radical equation √(2x+3) - √(x-10) = 4 using a brilliant and elegant two-equation strategy that completely avoids the chaos of squaring a two-term radical expression right away. Here is exactly how we do it: we introduce a companion equation √(2x+3) + √(x-10) = y, multiply both equations together to find y in terms of x using the difference of two squares, then add both equations to eliminate √(x-10), and finally square both sides to solve for x. We finish by checking all solutions to make sure they are valid. Every step is explained clearly and carefully so that anyone can follow along. This approach is clean, systematic, and far more elegant than the brute force method most textbooks teach. If you have ever struggled with radical equations, equations with square roots, or problems involving nested surds, this video will completely change the way you think about them. What you will learn in this video: How to introduce a companion equation to pair with a radical equation. How to multiply two conjugate radical expressions to eliminate surds. How to find y in terms of x using the difference of two squares identity. How to isolate and eliminate individual square root terms by adding equations. How to square both sides correctly and solve the resulting equation. Why checking solutions is not optional in radical equations and how extraneous solutions arise. This type of problem appears regularly in high school mathematics examinations, math olympiad competitions, college entrance exams, SAT and ACT advanced algebra sections, IB Mathematics, A-Level Mathematics, and university precalculus and algebra courses. The conjugate pairing technique demonstrated here is a powerful tool that applies to a wide range of radical and surd equations far beyond this specific problem. Whether you are a high school student preparing for exams, a university student brushing up on algebra, or a math enthusiast who simply loves discovering clever problem-solving strategies, this video has something valuable for you. The method is intuitive, the steps are easy to follow, and the result is deeply satisfying. Don’t forget to like 👍, subscribe    / @nonsomaths  , and hit the notification bell for more math tips and tricks! #maths #algebra #matholympiad #RadicalEquations #Surds #Precalculus #MathTutorial #MathTricks #HighSchoolMath #MathChallenge