1. Warm-up
Find the domain and range from these 3 equations.

3. Section 6-6 Radical Equations
Chapter 6
Section 6-6
Radical Equations

4. Objectives I can solve equations containing radicals
I can solve equations containing rational exponents
I can determine if a solution is Extraneous

5. Solving Radical Equations
Follow the same rules as any equation
Variable on left
Numbers on Right
Check your answers

6. Undoing The Square Root
We undo addition with subtraction
We undo multiplication with division
How do we undo the square root?
We square it!!

7. Undoing Radicals

8. Radical Equations
When solving radical equations make sure only the radical is on the left when you start the problem. (This is like solving absolute value)
ALWAYS Check answers. You may get Extraneous Solutions from radicals.

9. Example 1

10. Example 2

11. Example 3

12. Example 4 .

13. Undoing Rational Exponents
We undo the square root by Squaring It
We undo a rational exponent by using the Reciprocal of that exponent

14. Undoing Rational Exponents

15. Solve an equation with a rational exponent
EXAMPLE 4
Solve an equation with a rational exponent
Solve (x + 2)3/4 – 1 = 7.
(x + 2)3/4 – 1 = 7
Write original equation.
(x + 2)3/4 = 8
Add 1 to each side.
(x + 2)3/4
4/3
= 84/3
Raise each side to the power . 4 3
x + 2 = (23)4/3
Apply properties of exponents.
x + 2 = 24
Simplify.
x + 2 = 16
Simplify.
x = 14
Subtract 2 from each side.

16. Homework
Worksheet 10-5