In this video lesson, students build on their work with square roots to learn about a new mathematical idea, irrational numbers. Students recall the definition of rational numbers (MP6) and use this definition to search for a rational number x such that x² = 2. Students should not be left with the impression that looking for and failing to find a rational number whose square is 2 is a proof that  is irrational; this exercise simply reinforces what it means to be irrational and to provide plausibility for the claim. Students are not expected to prove that  is irrational.

Grade 8, Episode 23: Unit 8, Lesson 3 | Illustrative Math