1. 5.4 Solving Radical Equations and Inequalities

2. How to Solve Radical Equations
Find the obvious restrictions for the variable (optional).
Isolate the radical on one side of the equation.
Raise each side of the equation to the same exponent to eliminate the radical.
Solve the resulting equation using techniques you learned in previous chapters.
Check if the solutions fit the restrictions.
Plug the solutions in to the equation to
check for extraneous solutions.

3. Example 1
3 is within the restrictions, so it should be a real solution.
3 works for this equation, so it is not an extraneous solution.

4. Example 2
The air pressure at the center of the hurricane is about 938 millibars.

5. Example 3
Only -2 is within the restrictions so it is a real solution.
-8 does not work in this equation, so it is an extraneous solution.

6. Example 4
-5 does not work in this equation, so it is an extraneous solution.

7. Example 5

8. Example 6 Solve Square both sides rearrange divide by -2 Square again
YES

9. How to Solve Radical Inequalities
Example 7