This is a basic example illustrating how squaring both sides of an equation may introduce extraneous roots.
In this paper we have tried to connect algebra and geometry (2) with regard to extraneous roots, especially when both sides of an equation are squared.
The students in my class have difficulty coping with multiple new concepts and I believed that introducing a new way of showing 'applying an operation to both sides of an equation' could confuse many of the students in this class.