1. Questions about HW

2. 8.8 Solving Radical Equations and Inequalities
Review: Wednesday and Thursday
Ch. 8 Test: FRIDAY!

3. Objectives Solve radical equations. Solve radical inequalities.
8.8 Solving Radical Equations and Inequalities
Solve radical equations.
Solve radical inequalities.

4. Glossary Terms Principle of Powers radical equation radical inequality
8.8 Solving Radical Equations and Inequalities
Principle of Powers
radical equation
radical inequality

5. Rules and Properties Principle of Powers
8.8 Solving Radical Equations and Inequalities
Principle of Powers
If a = b and n is a positive integer,
then an = bn.

6. Rules and Properties Summary of Solving Radical Equations
8.8 Solving Radical Equations and Inequalities
Summary of Solving Radical Equations
1. Isolate the radical expression on one side of the equation.
2. Raise both sides of the equation to the appropriate power.
3. Repeat steps 1 and 2 to obtain an equation with no radical expressions.
4. Solve this equation.
5. Check solutions and discard extraneous solutions.

7. Key Skills Solve radical expressions. x + 1 = 3 (x + 1)2 = 32
8.8 Solving Radical Equations and Inequalities
Solve radical expressions.
x + 1 = 3
(x + 1)2 = 32
x + 1 = 9;
x = 8
Check:
8 + 1 = 3 ?
9 = 3
True

8. Example:
Solve Check your solution.

9. Example:
Solve . Check your solution.

10. Example:
Solve Check your solution.

11. Example:
Solve Check your solution.

12. Key Skills Solve radical inequalities. 3x – 2 > 2
8.8 Solving Radical Equations and Inequalities
Solve radical inequalities.
3x – 2 > 2
(3x – 2)2 > 22
3x – 2 > 4
x > 2
3x – 2
is defined for x > , so 2 3
the solution is x > 2.

13. Inequalities Example:
Solve Check your solution.
Remember: the radicand of a radical (the number/expression inside the square root) cannot be negative.