Square Root Investigation

by

Michelle Brantley

Objective: Students will become familiar with a visual image of square root in order to become more successful with the concept of square roots.

Materials: GSP

Time: 1-2 days

Level of Difficulty: Medium

Procedure:

NOTE: Go to the Display menu and click on Preferences. Make sure all the precision units are in tenths.

1) Construct a segment. Construct a perpendicular line to each of the endpoints of the line segment. Select the segment and one endpoint and construct a circle by center radius. Do this by pulling down the constuct menu and clicking on the circle by center + radius. Find the point at intersection. Now select the segment and the other endpoint. Construct another circle by center and radius. Connect the two points of intersection. Construct a line segment on each side of the square. Hide the circles and the lines. You should have a square.

2) Select the four vertices of the square. Construct the polygon interior. Measure the area of the polygon. Measure the distance of one side of the square. Now drag the lower right hand vertex so that the area of the polygon is four square units. What is the length of the side of the square?

3) You will now drag the vertex of the square to create the following areas. List the length of the side of the square for squares with the following areas.

AREA = 1 sq. cm. LENGTH = _________

AREA = 4 sq. cm. LENGTH = _________

AREA = 9 sq. cm. LENGTH = _________

AREA = 16 sq. cm. LENGTH = _________

AREA = 25 sq. cm. LENGTH = _________

AREA = 36 sq. cm. LENGTH = _________

AREA = 49 sq. cm. LENGTH = _________

AREA = 64 sq. cm. LENGTH = _________

AREA = 81 sq. cm. LENGTH = _________

AREA = 100 sq. cm. LENGTH = _________

AREA = 121 sq. cm. LENGTH = _________

AREA = 144 sq. cm. LENGTH = _________

4) What is the relationship between the area of the square and the length of the square's side? Describe in your own words the definition of a square root.

5) Now we are going to make a table using Geometer's Sketchpad. Drag the vertex so that the area of the square is 1 sq. cm. Record your data in the chart below. Repeat this process for areas 2, 3, 4, 5, 6, 7, 8, 9, and 10. Record all data below.

6) Under the GRAPH menu, click on show axes. Under the same menu, click on plot points. You will enter the coordinates from the table. Plot the points and notice the shape. Make a sketch below.