Lesson 4

Square Roots on the Number Line

Let’s explore square roots. 

Problem 1

  1. Find the exact length of each line segment.

    Linesegments AB and GH on grid. AB = square root 17, GH = square root 32.
  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.

quadrant 1, x axis, 0 to 10, by 1's. y axis, 0 to 8, by 1's. 


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. 

Scatter plot with line of best fit. Horizontal axis, assists, scale 0 to 60, by 15’s. Vertical axis, Points, scale 0 to 80, by 20’s. 
  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.)