What this lesson teaches
Real numbers rational and irrational.
Math in Action
Root 2 Irrational Proof
Prove that root 2 is irrational using contradiction!
Duration35 min
Age GroupAges 14–16
DifficultyAdvanced
SubjectMath
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The learning connection
Proof by contradiction is one of the most powerful logical tools in mathematics. Working through this specific proof — which created a genuine intellectual crisis in ancient Greece — builds appreciation for the rigour of mathematical truth and the courage required to follow logic wherever it leads.
Try it with your learner
1. Assume root 2 = p/q. 2. Square both sides. 3. Show 2 divides p. 4. Show 2 divides q. 5. Contradiction!