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Learn how to solve radical equations and inequalities with step-by-step examples. Practice solving equations and inequalities in a fun and interactive way.

jmcmahon
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  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.2w2 B. 2w C.w2 D. 5-Minute Check 4

  10. A.2w2 B. 2w C.w2 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. 82.6 kcal/day B. 156.8 kcal/day C. 826.5 kcal/day D. 1568.1 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. 82.6 kcal/day B. 156.8 kcal/day C. 826.5 kcal/day D. 1568.1 kcal/day 5-Minute Check 6

  15. 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. 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. Solve Radical Equations Example 1

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

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

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

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

  24. Square each side. Evaluate the squares. Original equation Check Replace x with 16. Simplify. Evaluate the square roots. Solve Radical Equations  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. 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. Solve a Cube Root Equation Original equation Subtract 5 from each side. Cube each side. Evaluate the cubes. Example 2

  30. 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. 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 Am = –2 Bm = 0 Cm = 12 Dm = 14 Example 3

  35. 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. 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. 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. 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. 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. Solve a Radical Inequality Check 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

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