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Nth Root and Simplifying Radicals

Learn about finding roots, simplifying radicals, and approximating radicals. Practice solving problems and applying the concepts in real-world scenarios.

christophercollins
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Nth Root and Simplifying Radicals

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

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

  13. 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

  14. 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

  15. 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. 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. Answer: Find Roots Example 1

  26. Find Roots Answer: Example 1

  27. Answer: Find Roots 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 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. Answer: Example 2

  35. 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

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

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

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

  44. 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

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

  46. 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

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

  48. 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

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

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