# Lesson 4

Square Roots on the Number Line

Let’s explore square roots.

### Problem 1

1. Find the exact length of each line segment.

2. Estimate the length of each line segment to the nearest tenth of a unit. Explain your reasoning.

### Problem 2

Plot each number on the $$x$$-axis: $$\sqrt{16},\text{ } \sqrt{35},\text{ } \sqrt{66}$$. Consider using the grid to help.

### Problem 3

Use the fact that $$\sqrt{7}$$ is a solution to the equation $$x^2 = 7$$ to find a decimal approximation of $$\sqrt{7}$$ whose square is between 6.9 and 7.1.

### Problem 4

Graphite is made up of layers of graphene. Each layer of graphene is about 200 picometers, or $$200 \times 10^{\text-12}$$ meters, thick. How many layers of graphene are there in a 1.6-mm-thick piece of graphite? Express your answer in scientific notation.

(From Unit 7, Lesson 14.)

### Problem 5

Here is a scatter plot that shows the number of assists and points for a group of hockey players. The model, represented by $$y = 1.5 x + 1.2$$, is graphed with the scatter plot.

1. What does the slope mean in this situation?
2. Based on the model, how many points will a player have if he has 30 assists?
(From Unit 6, Lesson 6.)

### Problem 6

The points $$(12, 23)$$ and $$(14, 45)$$ lie on a line. What is the slope of the line?

(From Unit 3, Lesson 5.)