1. Splash Screen

2. Five-Minute Check (over Lesson 6–6) CCSS Then/Now New Vocabulary
Key Concept: Solving Radical Equations
Example 1: Solve Radical Equations
Example 2: Solve a Cube Root Equation
Example 3: Standardized Test Example: Solve a Radical Equation
Key Concept: Solving Radical Inequalities
Example 4: Solve a Radical Inequality
Lesson Menu

3. A. B. C. D.
5-Minute Check 1

4. A. B. C. D.
5-Minute Check 1

5. A. 12
B. 8
C. 4
D. 2
5-Minute Check 2

6. A. 12
B. 8
C. 4
D. 2
5-Minute Check 2

7. A. B. C. D.
5-Minute Check 3

8. A. B. C. D.
5-Minute Check 3

9. A. 2w 2
B. 2w
C. w 2 D.
5-Minute Check 4

10. A. 2w 2
B. 2w
C. w 2 D.
5-Minute Check 4

11. A. B.
C. 5
D. 10
5-Minute Check 5

12. A. B.
C. 5
D. 10
5-Minute Check 5

13. The equation gives the approximate energy output y in kilocalories per day (kcal/day) for a reptile with a body mass m kilograms. The average mass of an alligator is 360 kilograms. Find the energy output of a reptile this size. Round your answer to the nearest tenth.
A kcal/day
B kcal/day
C kcal/day
D kcal/day
5-Minute Check 6

14. The equation gives the approximate energy output y in kilocalories per day (kcal/day) for a reptile with a body mass m kilograms. The average mass of an alligator is 360 kilograms. Find the energy output of a reptile this size. Round your answer to the nearest tenth.
A kcal/day
B kcal/day
C kcal/day
D kcal/day
5-Minute Check 6

15. Mathematical Practices 4 Model with mathematics.
Content Standards
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
Mathematical Practices
4 Model with mathematics.
CCSS

16. You solved polynomial equations.
Solve equations containing radicals.
Solve inequalities containing radicals.
Then/Now

17. radical equation
extraneous solution
radical inequality
Vocabulary

18. Concept

19. Add 1 to each side to isolate the radical.
Solve Radical Equations
A. Solve
Original equation
Add 1 to each side to isolate the radical.
Square each side to eliminate the radical.
Find the squares.
Add 2 to each side.
Example 1

20. Check Original equation Replace y with 38. Simplify.  Answer:
Solve Radical Equations
Check
Original equation
Replace y with 38. ?
Simplify. 
Answer:
Example 1

21. Answer: The solution checks. The solution is 38.
Solve Radical Equations
Check
Original equation
Replace y with 38. ?
Simplify. 
Answer: The solution checks. The solution is 38.
Example 1

22. B. Solve . Original equation Square each side. Find the squares.
Solve Radical Equations
B. Solve
Original equation
Square each side.
Find the squares.
Isolate the radical.
Divide each side by –4.
Example 1

23. Evaluate the square roots.
Solve Radical Equations
Square each side.
Evaluate the squares.
Original equation
Check
Replace x with 16.
Simplify.
Evaluate the square roots. 
Answer:
Example 1

24. Evaluate the square roots.
Solve Radical Equations
Square each side.
Evaluate the squares.
Original equation
Check
Replace x with 16.
Simplify.
Evaluate the square roots. 
Answer: The solution does not check, so there is no real solution.
Example 1

25. A. Solve
A. 19
B. 61
C. 67
D. no real solution
Example 1

26. A. Solve
A. 19
B. 61
C. 67
D. no real solution
Example 1

27. B. Solve
A. 2
B. 4
C. 9
D. no real solution
Example 1

28. B. Solve
A. 2
B. 4
C. 9
D. no real solution
Example 1

29. Subtract 5 from each side.
Solve a Cube Root Equation
In order to remove the power, or cube root, you must first isolate it and then raise each side of the equation to the third power.
Original equation
Subtract 5 from each side.
Cube each side.
Evaluate the cubes.
Example 2

30. Subtract 1 from each side.
Solve a Cube Root Equation
Subtract 1 from each side.
Divide each side by 3.
Check
Original equation
Replace y with –42.
Simplify.
The cube root of –125 is –5. 
Add.
Answer:
Example 2

31. Subtract 1 from each side.
Solve a Cube Root Equation
Subtract 1 from each side.
Divide each side by 3.
Check
Original equation
Replace y with –42.
Simplify.
The cube root of –125 is –5. 
Add.
Answer: The solution is –42.
Example 2

32. A. –14
B. 4
C. 13
D. 26
Example 2

33. A. –14
B. 4
C. 13
D. 26
Example 2

34. Solve a Radical Equation
A m = –2
B m = 0
C m = 12
D m = 14
Example 3

35. Raise each side to the sixth power.
Solve a Radical Equation
Original equation
Add 4 to each side.
Divide each side by 7.
Raise each side to the sixth power.
Evaluate each side.
Subtract 4 from each side.
Answer:
Example 3

36. Raise each side to the sixth power.
Solve a Radical Equation
Original equation
Add 4 to each side.
Divide each side by 7.
Raise each side to the sixth power.
Evaluate each side.
Subtract 4 from each side.
Answer: The answer is C.
Example 3

37. A. 221
B. 242
C. 266
D. 288
Example 3

38. A. 221
B. 242
C. 266
D. 288
Example 3

39. Concept

40. Solve a Radical Inequality
Since the radicand of a square root must be greater than or equal to zero, first solve 3x – 6  0 to identify the values of x for which the left side of the inequality is defined.
3x – 6  0
3x  6
x  2
Example 4

41. Original inequality Isolate the radical. Eliminate the radical.
Solve a Radical Inequality
Original inequality
Isolate the radical.
Eliminate the radical.
Add 6 to each side.
Divide each side by 3.
Answer:
Example 4

42. Answer: The solution is 2  x  5.
Solve a Radical Inequality
Original inequality
Isolate the radical.
Eliminate the radical.
Add 6 to each side.
Divide each side by 3.
Answer: The solution is 2  x  5.
Example 4

43. Only the values in the interval 2  x  5 satisfy the inequality.
Solve a Radical Inequality
Check
Test some x-values to confirm the solution. Let Use three test values: one less than 2, one between 2 and 5, and one greater than 5.
Only the values in the interval 2  x  5 satisfy the inequality.
Example 4

44. A. B. C. D.
Example 4

45. A. B. C. D.
Example 4

46. End of the Lesson