Lesson 4
Square Roots on the Number Line
Let’s explore square roots.
Problem 1
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Find the exact length of each line segment.
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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.](https://cms-im.s3.amazonaws.com/x9jTyGudkLV1vswPXUV3MT9e?response-content-disposition=inline%3B%20filename%3D%228-8.8.B.4.revised.image.06.taller.png%22%3B%20filename%2A%3DUTF-8%27%278-8.8.B.4.revised.image.06.taller.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20250121%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250121T123255Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d4e62a4659ddef43caa2abe723efd2289fc9d724ecc480640b7569f39379c48c)
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.
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.](https://cms-im.s3.amazonaws.com/WBDBNoi5NWr7kJmrkFdWEzyL?response-content-disposition=inline%3B%20filename%3D%228-8.6.A2.PP.hockeypointstrend.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6.A2.PP.hockeypointstrend.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20250121%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250121T123255Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d23cff465cf29582cd1be2d8d7d96aa5b34b02067e89754c19280e9f26e3585e)
- 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?