A geometric approach using exact square manipulatives can promote an understanding of the algorithm to dismantle radical expressions.
Kyle T. Schultz and Stephen F. Bismarck
Emiliano Gómez and Risa A. Wolfson
In this activity, students gradually fill bottles of different shapes and graph the water level (height) versus the volume of water inside the bottles. Then they explore the relationship between the shape of a bottle and the resulting graph.