Algebra

Chapter 7, Lines and Distance

Superlesson 7-2, Square Roots

Let's explore lines, distance, and a very interesting mathematician, Pythagoras!

Part A, Square Roots

1. Read through the Pythagoras Web site.

a. Write two ideas you have gleaned from the reading about Pythagoras' life, teachings, or discoveries.

Part B, Square Root Functions and Equations

2. Open the Circle and Square Web site. Using a compass, a straight edge, and the circular model as a guide, reproduce the circular model for the square root of 2 on a piece of 8 1/2 " x 11" paper. Make the radius of your circle between 10 and 20 centimeters.

a. Measure the length of your square to the nearest centimeter.

b. Measure the diagonal of your square to the nearest centimeter.

c. Using your calculator, find the approximate ratio of the length of the diagonal of your square to the length of the side of your square?

d. Compare your answers to c with those obtained by other students. What do you notice?

Part C, Making Connections

3. Explain why the square root of two is not rational.

4. Explain why the square root of four is rational.

5. Is the square root of 12.96 rational or irrational? Explain.