1. Splash Screen

2. Five-Minute Check (over Lesson 6–3) CCSS Then/Now New Vocabulary
Key Concept: Definition of nth Root
Key Concept: Real nth Roots
Example 1: Find Roots
Example 2: Simplify Using Absolute Value
Example 3: Real-World Example: Approximate Radicals
Lesson Menu

3. A. B. C.
D. D = {x | x ≤ –2}, R = {y | y ≥ 0}
5-Minute Check 1

4. A. B. C.
D. D = {x | x ≤ –2}, R = {y | y ≥ 0}
5-Minute Check 1

5. A. B. C. D.
5-Minute Check 2

6. A. B. C. D.
5-Minute Check 2

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

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

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

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

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

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

13. The point (3, 6) lies on the graph of Which ordered pair lies on the graph ofB.
C. (2, –2)
D. (–2, 2)
5-Minute Check 6

14. The point (3, 6) lies on the graph of Which ordered pair lies on the graph ofB.
C. (2, –2)
D. (–2, 2)
5-Minute Check 6

15. Mathematical Practices 6 Attend to precision.
Content Standards
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
Mathematical Practices
6 Attend to precision.
CCSS

16. You worked with square root functions.
Simplify radicals.
Use a calculator to approximate radicals.
Then/Now

17. nth root
radical sign
index
radicand
principal root
Vocabulary

18. Concept

19. Concept

20. Find Roots
= ±4x4
Answer:
Example 1

21. Answer: The square roots of 16x8 are ±4x4.
Find Roots
= ±4x4
Answer: The square roots of 16x8 are ±4x4.
Example 1

22. Find Roots
Answer:
Example 1

23. Find Roots
Answer: The opposite of the principal square root of (q3 + 5)4 is –(q3 + 5)2.
Example 1

24. Find Roots
Answer:
Example 1

25. Find Roots
Answer:
Example 1

26. Find Roots
Answer:
Example 1

27. Find Roots
Answer:
Example 1

28. A. Simplify
A. ±3x6
B. ±3x4
C. 3x4
D. ±3x2
Example 1

29. A. Simplify
A. ±3x6
B. ±3x4
C. 3x4
D. ±3x2
Example 1

30. B. Simplify . A. –(a3 + 2)4 B. –(a3 + 2)8 C. (a3 + 2)4 D. (a + 2)4
Example 1

31. B. Simplify . A. –(a3 + 2)4 B. –(a3 + 2)8 C. (a3 + 2)4 D. (a + 2)4
Example 1

32. C. Simplify
A. 2xy2
B. ±2xy2
C. 2y5
D. 2xy
Example 1

33. C. Simplify
A. 2xy2
B. ±2xy2
C. 2y5
D. 2xy
Example 1

34. Simplify Using Absolute Value
Note that t is a sixth root of t 6. The index is even, so the principal root is nonnegative. Since t could be negative, you must take the absolute value of t to identify the principal root.
Answer:
Example 2

35. Simplify Using Absolute Value
Note that t is a sixth root of t 6. The index is even, so the principal root is nonnegative. Since t could be negative, you must take the absolute value of t to identify the principal root.
Answer:
Example 2

36. Since the index is odd, you do not need absolute value.
Simplify Using Absolute Value
Since the index is odd, you do not need absolute value.
Answer:
Example 2

37. Since the index is odd, you do not need absolute value.
Simplify Using Absolute Value
Since the index is odd, you do not need absolute value.
Answer:
Example 2

38. A. Simplify
A. x
B. –x
C. |x|
D. 1
Example 2

39. A. Simplify
A. x
B. –x
C. |x|
D. 1
Example 2

40. B. Simplify . A. |3(x + 2)3| B. 3(x + 2)3 C. |3(x + 2)6| D. 3(x + 2)6
Example 2

41. B. Simplify . A. |3(x + 2)3| B. 3(x + 2)3 C. |3(x + 2)6| D. 3(x + 2)6
Example 2

42. Understand You are given the value for k.
Approximate Radicals
A. SPACE Designers must create satellites that can resist damage from being struck by small particles of dust and rocks. A study showed that the diameter in millimeters d of the hole created in a solar cell by a dust particle traveling with energy k in joules is about Estimate the diameter of a hole created by a particle traveling with energy 3.5 joules.
Understand You are given the value for k.
Plan Substitute the value for k into the formula. Use a calculator to evaluate.
Example 3A

43. Solve Original formula
Approximate Radicals
Solve Original formula
k = 3.5
Use a calculator.
Answer:
Example 3A

44. Solve Original formula
Approximate Radicals
Solve Original formula
k = 3.5
Use a calculator.
Answer: The hole created by a particle traveling with energy of 3.5 joules will have a diameter of approximately millimeters.
Example 3A

45. Check Original equation
Approximate Radicals
Check Original equation
Add to each side.
Divide both sides by
Cube both sides.
Simplify.
Example 3A

46. Approximate Radicals
B. SPACE Designers must create satellites that can resist damage from being struck by small particles of dust and rocks. A study showed that the diameter in millimeters d of the hole created in a solar cell by a dust particle traveling with energy k in joules is about If a hole has diameter of 2.5 millimeters, estimate the energy with which the particle that made the hole was traveling.
Example 3B

47. Solve Original formula
Approximate Radicals
Solve Original formula
d = 2.5
Use a calculator.
Answer:
Example 3B

48. Solve Original formula
Approximate Radicals
Solve Original formula
d = 2.5
Use a calculator.
Answer: The hole with a diameter of 2.5 millimeters was created by a particle traveling with energy of 23.9 joules.
Example 3B

49. A. PHYSICS The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. Find the value of T for a 2-foot-long pendulum.
A. about 0.25 second
B. about 1.57 seconds
C. about seconds
D. about seconds
Example 3A

50. A. PHYSICS The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. Find the value of T for a 2-foot-long pendulum.
A. about 0.25 second
B. about 1.57 seconds
C. about seconds
D. about seconds
Example 3A

51. B. PHYSICS The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. How long is the pendulum if it takes 5 seconds to swing back and forth?
A. about 2.5 feet
B. about 10 feet
C. about 20.3 feet
D. about 25.5 feet
Example 3B

52. B. PHYSICS The time T in seconds that it takes a pendulum to make a complete swing back and forth is given by the formula where L is the length of the pendulum in feet and g is the acceleration due to gravity, 32 feet per second squared. How long is the pendulum if it takes 5 seconds to swing back and forth?
A. about 2.5 feet
B. about 10 feet
C. about 20.3 feet
D. about 25.5 feet
Example 3B

53. End of the Lesson