1. 8.1 Square Roots and the Pythagorean Theorem

2. Square Root

3. Square Root

4. Example Find each square root. a. b. c. d. e. f. g. h.

5. Approximating Square Root The period of a pendulum is the time required for the pendulum to swing back and forth to complete one cycle. The period t (in seconds) is a function of the pendulum’s length l (in feet), which is defined by t = f (l ) = 1.11 Find the period of a pendulum that is 5 feet long.

6. Example – Solution We substitute 5 for l in the formula and simplify. t = 1.11 = 1.11  1.11 (2.24)  2.48 The period is approximately 2.5 seconds for a 5- foot-long pendulum.

7. Rational, Irrational, or Imaginary

8. Imaginary Number

9. Example Determine whether the following are rational, irrational, or imaginary. a. b. c.

10. Example Graph: Solution: To graph this function, we make a table of values and plot each pair of points.

11. Pythagorean Theorem Given a right triangle: Hypotenuse is the side opposite the right angle and is the longest side. Legs of the (right) triangle are the other 2 sides. Pythagorean Theorem: c 2 = a 2 + b 2

12. Example – Building A High-Ropes Adventure Course The builder of a high-ropes course wants to stabilize the pole shown by attaching a cable from a ground anchor 20 feet from its base to a point 15 feet up the pole. How long will the able be?

13. Example – Building A High-Ropes Adventure Course

14. Your Turn