How do you teach students to evaluate square roots of small perfect squares and cube roots of small perfect cubes? The foundational concept behind evaluating roots is the connection between side length of a square and its area or edge length of a cube and its volume. Do you stop there? No need. Start with the geometric connection and then extend to a visual proof that the square root of 2 is irrational. This investigation will pave the road to move

approximating irrational numbers from concrete to abstract understanding...which is a natural prerequisite to the Pythagorean theorem.

This investigation highlights Common Core State Standard 8.EE.A.2 included in MATH-8 and Accelerated MATH-7.

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