The problem here was a similar type of problem I submitted as a Math league competition problem to my school. When students first see an equation with a square root, the first inclination for some students is to remove the square root by squaring both sides. However, there are certain type of problems where it would be much easier to solve by making one side of the equation as a perfect square. This would eliminate one of the square roots.
The goal is to make the radicand of the larger square root into a perfect square. After this is accomplished, everything else is easy because all the Algebra process will fall in place. Sometimes these types of problems are overlooked in favor of the more direct route of square both sides to remove the square root. This happens for two reasons. The first reason is teachers sometimes are restricted with time. These type of problems tend to be the more difficult problems and are used as bonus type problems. The other reason is sometimes students are ore not ready to see this type of problems when they are registered for the class. With time constraints and the level of the class, A or B type of problems are normally used and the more difficult C level problems are sometimes used only for bonus problems.
Mathematics is such a wonderful universal language.