Lesson 4Square Roots on the Number Line
Learning Goal
Let’s explore square roots.
Learning Targets
I can find a decimal approximation for square roots.
I can plot square roots on the number line.
Lesson Terms
- rational number
- square root
Warm Up: Diagonals
Problem 1
What do you notice? What do you wonder?
Activity 1: Squaring Lines
Problem 1
Estimate the length of the line segment to the nearest tenth of a unit (each grid square is 1 square unit).
Problem 2
Find the exact length of the segment.
Activity 2: Square Root of 3
Problem 1
Diego said that he thinks that
Use the square to explain why 2.5 is not a very good approximation for
. Find a point on the number line that is closer to . Draw a new square on the axes and use it to explain how you know the point you plotted is a good approximation for . Use the fact that
is a solution to the equation to find a decimal approximation of whose square is between 2.9 and 3.1.
Are you ready for more?
Problem 1
A farmer has a grassy patch of land enclosed by a fence in the shape of a square with a side length of 4 meters. To make it a suitable home for some animals, the farmer would like to carve out a smaller square to be filled with water, as in the figure.
What should the side length of the smaller square be so that half of the area is grass and half is water?
Lesson Summary
Here is a line segment on a grid. What is the length of this line segment?
By drawing some circles, we can tell that it’s longer than 2 units, but shorter than 3 units.
To find an exact value for the length of the segment, we can build a square on it, using the segment as one of the sides of the square.
The area of this square is 5 square units. (Can you see why?) That means the exact value of the length of its side is
Notice that 5 is greater than 4, but less than 9. That means that
With some arithmetic, we can get an even more precise idea of where