Explore the applet using the sliders. Notice how each of the slider affect the two shapes.[br]Answer the questions below.
What changes and what stays the same when you move Slider [math]X_n[/math]?
What changes and what stays the same when you move Slider S?
What does the value of the Slider S represent?
What does Slider [math]X_n[/math] represent?
How are the square and the rectangle related?
What does the "Next Iteration" do?
Click “Next Iteration” several times. Record the values of X_n and the other side of the rectangle. Describe what happens to the rectangle after each click.
From your observations, write the rule for finding the next estimate x_{n+1} from the current estimate x_n.
Explain why the repeated process gives an approximation of √S. Use the rectangle, the square, and the formula in your explanation.
Give an approximate value for √40. Show at least three iterations and explain what each number represents.