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.

CCSS Standards


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: \(\frac74,0,\frac63,0.2,\text-\frac13,\text-5,\sqrt9\)

  • 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.