Lesson 5
Reasoning About Square Roots
Lesson Narrative
The purpose of this lesson is to encourage students to reason about square roots and reinforce the idea that they are numbers on a number line. This lesson continues students’ move from geometric to algebraic characterizations of square roots.
Learning Goals
Teacher Facing
 Comprehend that $\text\sqrt{a}$ represents the opposite of $\sqrt{a}$.
 Determine a solution to an equation of the form $x^2=a$ and represent the solution as a point on the number line.
 Identify the two whole number values that a square root is between and explain (orally) the reasoning.
Student Facing
Let’s approximate square roots.
Learning Targets
Student Facing
 When I have a square root, I can reason about which two whole numbers it is between.
Glossary Entries

irrational number
An irrational number is a number that is not a fraction or the opposite of a fraction.
Pi (\(\pi\)) and \(\sqrt2\) are examples of irrational numbers.

rational number
A rational number is a fraction or the opposite of a fraction.
Some examples of rational numbers are: \(\frac74,0,\frac63,0.2,\text\frac13,\text5,\sqrt9\)

square root
The square root of a positive number \(n\) is the positive number whose square is \(n\). It is also the the side length of a square whose area is \(n\). We write the square root of \(n\) as \(\sqrt{n}\).
For example, the square root of 16, written as \(\sqrt{16}\), is 4 because \(4^2\) is 16.
\(\sqrt{16}\) is also the side length of a square that has an area of 16.