1. Solving Radical Equations
Brett Solberg
AHS ‘11-’12

2. Warm-up Write with rational exponents 1) 7 𝑥 3 𝑦 2 𝑧 2 2) 3𝑚𝑛 3
1) 7 𝑥 3 𝑦 2 𝑧 2
2) 3𝑚𝑛 3
3) Solve for x x2 + 6x + 8 = 0
What HW problems should we review?

3. Today’s Agenda HW Review Solving Radicals
Isolating Radicals
Get out your notes and extra paper

4. The Principle of Powers
If x = 5
Then x2 = 52
If 𝑥 = 5
Then ( 𝑥) 2 = 52
If −𝑥 = x + 5
Then ( 2 −𝑥 )2 = (x + 5)2

5. Steps to Solving Radical Expressions
Isolate the radical
Rationalize the radical
Solve
Check your work
𝑥 - 3 = 4
𝑥 = 7 Isolate the radical
( 𝑥 )2 = Rationalize the radical
x = 49 Solve
= 4 Check your work
7 – 3 = 4 4 = 4

6. Examples
𝑥 - 7 = 3
3𝑥+4 = 5

7. Extraneous Roots x = 𝑥+7 + 5 Why did one of the solutions not work?
Solutions that don’t check are called extraneous solutions

8. x – 5 = 18 −2𝑥
x – 2 = 2𝑥 −1

9. What if there’s more than one radical?
Plan A – Combine Radicals
3 𝑥 = 2 𝑥 - 1

10. What if there’s more than one radical?
Plan B – Solve one radical at a time
3 𝑥 = 2 𝑥 - 1

11. 𝑥 − 𝑥 = 1

12. Other Radicals
3 𝑥 = 5
3 𝑥 − = 7

13. Beach If I stand on the beach, how far can I see? d = 1.2 ℎ
d = distance miles
h = height in feet

14. Summary
Isolate
Rationalize
Solve
Check

15. Homework 7.6 pg 319 #1 – 33, 43 – 45 Midyear Review:
going on this quarter
correct it in class on Thu