1. 5-8 solving radical equations and inequalities
Chapter 5
5-8 solving radical equations and inequalities

2. objectives
Solve radical equations and inequalities.

3. radical
A radical equation contains a variable within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a power.

4. Steps to solve

5. Example#1
Solve each equation.

6. Example#2
Solve each equation

7. Example
Solve

8. example
Solve

9. Solving radicals with extraneous solutions
Raising each side of an equation to an even power may introduce extraneous solutions.

10. Example Solve Method 1 Use a graphing calculator.
Let Y1 = and Y2 = 5 – x.
The graphs intersect in only one point, so there is exactly one solution.
The solution is x = – 1

11. continue
Method 2 Use algebra to solve the equation.

12. example
Solve

13. example
Solve

14. Solving equations with rational exponents
Solve 1 3
(5x + 7) = 3

15. examples
Solve
2x = (4x + 8) 1 2

16. example
Solve 1 2
(2x + 15) = x

17. Radical inequalities
A radical inequality is an inequality that contains a variable within a radical. You can solve radical inequalities by graphing or using algebra.

18. example Solve . Method 1 Use a graph and a table.
On a graphing calculator, let Y1 = and Y2 = 9. The graph of Y1 is at or below the graph of Y2 for values of x between 3 and 21. Notice that Y1 is undefined when < 3.
The solution is 3 ≤ x ≤ 21.

19. continue
Method 2 Use algebra to solve the inequality.

20. example
Solve

21. application
The speed s in miles per hour that a car is traveling when it goes into a skid can be estimated by using the formula s = , where f is the coefficient of friction and d is the length of the skid marks in feet.
A car skids to a stop on a street with a speed limit of 30 mi/h. The skid marks measure 35 ft, and the coefficient of friction was 0.7. Was the car speeding? Explain.

22. Student guided practice
Do even problems in your book page 380

23. Homework
Do even problems from in your book page 381