Abstract
In the classroom, a recurring question often arises: “Are we allowed to do this with square roots — and what about that?” This led us to search for wordless proofs that help visualize both the rules that are allowed and those that are not when working with square roots. These “wordless proofs” invite us to rediscover the geometric meaning of algebra: to multiply or divide is to enlarge or shrink a square. They allow students to guess before proving, and remind us that a well-chosen image can be worth many lines of algebra in the reasoning process. In this article, we present three such visual demonstrations, hoping to offer a new way for students to understand and internalize the behavior of square roots.
Keywords
Square Roots, Visual Proof, Wordless Proof, Geometric Reasoning, Secondary Mathematics
How to Cite
Svoboda, H. & Roustan, V., (2026) “Silent Geometry, Talking Roots”, Ohio Journal of School Mathematics 103(1): 8, 88-91. doi: https://doi.org/10.18061/ojsm.6932