1. 5.7 R ATIONAL E XPONENTS 5.8 R ADICAL EQUATIONS Algebra II w/ trig

2. Rational (fraction) exponents can be rewritten in radical form, and radicals can be rewritten in rational form.

3. I. Write in radical form. A.B.C. D.E.

4. II. Write in exponential form. A.B.C. D.E.

5. III. Evaluate. A.B. C.D.

6. E.F.

7. IV. Conditions for a simplified expression --it has no negative exponents --it has no fractional exponents in denominator --it is not a complex fraction --the index of any remaining radical is small as possible ***if the original problem is in radical form, the answer should be in radical form *** ***If the problem is in rational exponent form, the answer should be in rational form ***

8. A.B.

9. C.D.

10. E.F.

11. 5.8 R ATIONAL EXPRESSIONS I. Definitions: 1. Radical equations is an equation that has a variable in a radicand. Ex: Not: 2. Extraneous solutions is a solution that does not satisfy the original equation. You can only determine if a solution is extraneous by checking your answer.

12. II. Steps to Solving Radical Equations: 1. Isolate the radical if possible. 2. To eliminate the radical, raise each side of the equation to a power equal to the index of the radical. 3. Solve the resulting equation. 4. Check for extraneous solutions.

13. III. Solving a simple radical equation. A.B.

14. C.D.

15. IV. Solving an equation with one radical. A.B.

16. V. Solving an Equation with two radicals. A.

17. VI. Radical Inequalities A. Definition: an inequality that has a variable in a radicand. B. STEPS 1. Since the value of the radicand must be greater than or equal to zero, first set the radicand > to zero, to identify the values for which the left side of the given inequality is defined. 2. Now solve the original inequality, to identify the values for which the right side of the inequality is defined. A. Isolate the radical B. Eliminate the radical C. Solve the remaining equation. 3. Use the left and right side values to determine three regions. Pick a test point within each region to determine if the inequality is true in that region. 4. Summarize your solution in set notation and a graph.

18. VII. Solve the following Radical Inequalities 1.

19. 2.