Lesson 4
Square Roots on the Number Line
Let’s explore square roots.
Problem 1

Find the exact length of each line segment.

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 \(200 \times 10^{\text12}\) meters, thick. How many layers of graphene are there in a 1.6mmthick piece of graphite? Express your answer in scientific notation.
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.
 What does the slope mean in this situation?
 Based on the model, how many points will a player have if he has 30 assists?
Problem 6
The points \((12, 23)\) and \((14, 45)\) lie on a line. What is the slope of the line?