1. Splash Screen

2. Lesson Menu 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

3. Over Lesson 6–3 5-Minute Check 1 A. B. C. D.D = {x | x ≤ –2}, R = {y | y ≥ 0}

4. Over Lesson 6–3 5-Minute Check 2 A. B. C. D.

5. Over Lesson 6–3 5-Minute Check 3 A. B. C. D.

6. Over Lesson 6–3 5-Minute Check 4 A. B. C. D.

7. Over Lesson 6–3 5-Minute Check 5 C. D. A. B.

8. Over Lesson 6–3 5-Minute Check 6 A. B. C.(2, –2) D.(–2, 2) The point (3, 6) lies on the graph of Which ordered pair lies on the graph of

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

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

11. Vocabulary nth root radical sign index radicand principal root

12. Concept

14. Example 1 Find Roots = ±4x 4 Answer: The square roots of 16x 8 are ±4x 4.

15. Example 1 Find Roots Answer: The opposite of the principal square root of (q 3 + 5) 4 is –(q 3 + 5) 2.

16. Example 1 Find Roots Answer:

17. Example 1 Find Roots Answer:

18. Example 1 A.±3x 6 B.±3x 4 C.3x 4 D.±3x 2 A. Simplify.

19. Example 1 A.–(a 3 + 2) 4 B. –(a 3 + 2) 8 C.(a 3 + 2) 4 D.(a + 2) 4 B. Simplify.

20. Example 1 A.2xy 2 B.±2xy 2 C.2y 5 D.2xy C. Simplify.

21. Example 1 A.–4 B.±4 C.–2 D.±4i D. Simplify.

22. Example 2 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:

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

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

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

26. Example 3A Approximate Radicals UnderstandYou are given the value for k. 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. PlanSubstitute the value for k into the formula. Use a calculator to evaluate.

27. Example 3A Approximate Radicals k = 3.5 Answer: The hole created by a particle traveling with energy of 3.5 joules will have a diameter of approximately 1.237 millimeters. Use a calculator. SolveOriginal formula

28. Example 3A Approximate Radicals Add 0.169 to each side. Divide both sides by 0.926. Cube both sides. Simplify. CheckOriginal equation

29. Example 3B 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.

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

31. Example 3A A.about 0.25 second B.about 1.57 seconds C.about 12.57 seconds D.about 25.13 seconds 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.

32. Example 3B A.about 2.5 feet B.about 10 feet C.about 20.3 feet D.about 25.5 feet 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?

33. End of the Lesson