# Lesson 5

### 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.

### 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: $$\frac74,0,\frac63,0.2,\text-\frac13,\text-5,\sqrt9$$

• 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.