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Goal: simplify sqrt(72) from Card B and verify by squaring. Say: “We may split a product under a nonnegative square root, not a sum.”
0–2: Recall that sqrt(36)=6.
2–7: Model 72=36×2, so sqrt(72)=sqrt(36)sqrt(2)=6sqrt(2).
7–13: Learners explain why sqrt(36)+sqrt(2) is not equivalent; compare squares or approximate values.
13–20: Independent simplification with square-factor mat, then square the result: (6sqrt(2))^2=72.
20–25: Ask why the answer lies between 8 and 9 despite its exact radical form.
Routes: symbolic factor-and-check; spoken factor tree with recorded equation; arrange a 36×2 rectangle card and label the equal roots. Other domains:Day 2 swaps. Optional/home: make three factor pairs for 72 and find why the largest square factor is most efficient. Move: if a student writes sqrt(a+b)=sqrt(a)+sqrt(b), test it at a=b=1 and contrast sqrt(ab).