Lesson 3

In previous lessons, students learned that square root notation is used to write the side length of a square given the area of the square. For example, a square whose area is 17 square units has a side length of \(\sqrt{17}\) units.

In this 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 \(x^2 = 2\). 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 \(\sqrt{2}\) is irrational; this exercise is simply meant to reinforce what it means to be irrational and to provide some plausibility for the claim. Students are not expected to prove that \(\sqrt{2}\) is irrational in grade 8, and so ultimately must just accept it as a fact for now.

In the next lesson, students will learn strategies for finding the approximate location of an irrational number on a number line.

It would be useful throughout this unit to have a list of perfect squares for easy reference. Consider hanging up a poster that shows the 20 perfect squares from 1 to 400. It is particularly handy in this lesson.