1. Section 9.4 Solving Equations Containing Radical Expressions

2. 9.4 Lecture Guide: Solving Equations Containing Radical Expressions Objective: Solve equations involving radical expressions.

3. Power Theorem Algebraically If x = y, then Verbally If two expressions are equal, then their nth powers are equal. Example then but Caution: The equations x = y and are not always equivalent. The equation can have a solution that is not a solution of x = y. If For any real numbers x and y and natural number n :

4. Solving Radical Equations Containing a Single Radical To solve equations containing radical expressions, we will use the power theorem, which states that if two expressions are equal, then their nth powers are equal. For example, if then ProcedureExample Step 1. Isolate a radical term on one side of the equation. Step 2. Raise both sides to the nth power. Step 3. Solve the resulting equation.* Step 4. Check the possible solutions in the original equation to determine whether they are really solutions or are extraneous. * If this equation contains a radical, repeat Steps 1 and 2.

5. Solve each equation. 1.

6. Solve each equation. 2.

7. Solve each equation. 3.

8. Solve each equation. 4.

9. Solve each equation. 5.

10. Solve each equation. 6.

11. Solve each equation. 7.

12. Solve each equation. 8.

13. 9. Use the table and graph to determine the solution of the equation Solution based on table and graph: __________ Solve this equation algebraically.

14. Determine the exact x- and y-intercepts of the graph of each function. 10.

15. Determine the exact x- and y-intercepts of the graph of each function. 11.

16. The Pythagorean Theorem: If triangle ABC is a right triangle, then

17. Use the Pythagorean Theorem to find the length of the side that is not given. 12. b 26 24

18. Use the Pythagorean Theorem to find the length of the side that is not given. 13. 36 c 15

19. Objective: Calculate the distance between two points.

20. Distance Formula The distance d betweenandis given by

21. Plot each pair of points and then calculate the distance between these points: 14.and

22. Plot each pair of points and then calculate the distance between these points: 15.and

23. Calculate the distance between these points: 16.and

24. Calculate the distance between these points: 17.and

25. 18. Find all points with an x-coordinate of 3 that are 10 units away from the point Hint: Use the grid below to help.

26. 19. An extension cord is plugged into an outlet at point A on the side of a house. The owner of the house is running an electric weed trimmer to trim along a fence that runs parallel to the side of the house 40 ft away. (a) Write a function L(x) that gives the length of the extension cord needed to reach any point C along the fence, where x is the distance from B to C and the line segment from A to B is perpendicular to the side of the house.

27. 19. An extension cord is plugged into an outlet at point A on the side of a house. The owner of the house is running an electric weed trimmer to trim along a fence that runs parallel to the side of the house 40 ft away. (b) Evaluate and interpret L(25).

28. 19. An extension cord is plugged into an outlet at point A on the side of a house. The owner of the house is running an electric weed trimmer to trim along a fence that runs parallel to the side of the house 40 ft away. (c) If point D is 29 ft from point B, will a 50 ft extension cord allow the owner to reach point D?