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 Over Lesson 6–6 A. B. C. D. Over Lesson 6–6 A. 12 B. 8 C. 4 D. 2 Over Lesson 6–6 A. B. C. D. Over Lesson 6–6 A. 2w 2 B. 2w C. w 2 D. Over Lesson 6–6 A. B. C. 5 D. 10 Over Lesson 6–6 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 Content Standards A.SSE.2 Use the structure of an expression to identify ways to rewrite it. Mathematical Practices 4 Model with mathematics. You solved polynomial equations. • Solve equations containing radicals. • Solve inequalities containing radicals. • radical equation • extraneous solution • radical inequality Solve Radical Equations 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 Check Original equation ? Replace y with 38. Simplify. Answer: The solution checks. The solution is 38. Solve Radical Equations B. Solve . Original equation Square each side. Find the squares. Isolate the radical. Divide each side by –4. Solve Radical Equations Square each side. Evaluate the squares. Original equation Check Replace x with 16. Simplify. Evaluate the square roots. Answer: The solution does not check, so there is no real solution. A. Solve A. 19 B. 61 C. 67 D. no real solution . B. Solve A. 2 B. 4 C. 9 D. no real solution . Solve a Cube Root Equation 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. Original equation Subtract 5 from each side. Cube each side. Evaluate the cubes. 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. A. –14 B. 4 C. 13 D. 26 Solve a Radical Equation A m = –2 B m=0 C m = 12 D m = 14 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. A. 221 B. 242 C. 266 D. 288 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 x2 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. Solve a Radical Inequality Check 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. Only the values in the interval 2 x 5 satisfy the inequality. A. B. C. D.