This complete 2 day lesson includes all the materials that need to be duplicated for students to visualize what it means to simplify a radical or a square root. The lesson is developed based on the area model. Students begin by building squares with areas such as 9 and 16 to notice the sides of the square have sides of 3 or 4. This shows students that if they want to find the square root they are really building a square that holds the area and then the length of the side the square is the answer for the square root.
Building on this concept students use provided manipulatives to build square that hold area such as 8 to discover that the length of the side is made up of 3 square roots of 2. Study the preview pages to notice how this is done.
Students create visuals for 20 different square roots and then observe that to simplify a radical they need to look for a perfect square factor.