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

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  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. 5-Minute Check 2

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

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

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

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

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

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

  11. nth root • radical sign • index • radicand • principal root Vocabulary

  12. Concept

  13. Concept

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

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

  16. Answer: Find Roots Example 1

  17. Answer: Find Roots Example 1

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

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

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

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

  22. Answer: Simplify Using Absolute Value Note that t is a sixth root of t6. 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. Example 2

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

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

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

  26. A. SPACEDesigners 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. Approximate Radicals Understand You are given the value for k. Plan Substitute the value for k into the formula. Use a calculator to evaluate. Example 3A

  27. Solve Original formula Approximate Radicals 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 1.237 millimeters. Example 3A

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

  29. B. SPACEDesigners 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. Approximate Radicals Example 3B

  30. Solve Original formula Approximate Radicals 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

  31. 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 12.57 seconds D. about 25.13 seconds Example 3A

  32. 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

  33. End of the Lesson

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