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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

A. B. C. D. 5-Minute Check 1

A. B. C. D. 5-Minute Check 1

A. 12 B. 8 C. 4 D. 2 5-Minute Check 2

A. 12 B. 8 C. 4 D. 2 5-Minute Check 2

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

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

A. 2w 2 B. 2w C. w 2 D. 5-Minute Check 4

A. 2w 2 B. 2w C. w 2 D. 5-Minute Check 4

A. B. C. 5 D. 10 5-Minute Check 5

A. B. C. 5 D. 10 5-Minute Check 5

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

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

Mathematical Practices 4 Model with mathematics. Content Standards A.SSE.2 Use the structure of an expression to identify ways to rewrite it. Mathematical Practices 4 Model with mathematics. CCSS

You solved polynomial equations. Solve equations containing radicals. Solve inequalities containing radicals. Then/Now

radical equation extraneous solution radical inequality Vocabulary

Concept

Add 1 to each side to isolate the radical. 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. Example 1

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

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

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

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

Evaluate the square roots. 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. Example 1

A. Solve . A. 19 B. 61 C. 67 D. no real solution Example 1

A. Solve . A. 19 B. 61 C. 67 D. no real solution Example 1

B. Solve . A. 2 B. 4 C. 9 D. no real solution Example 1

B. Solve . A. 2 B. 4 C. 9 D. no real solution Example 1

Subtract 5 from each side. 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. Example 2

Subtract 1 from each side. 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

Subtract 1 from each side. 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

A. –14 B. 4 C. 13 D. 26 Example 2

A. –14 B. 4 C. 13 D. 26 Example 2

Solve a Radical Equation A m = –2 B m = 0 C m = 12 D m = 14 Example 3

Raise each side to the sixth power. 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

Raise each side to the sixth power. 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

A. 221 B. 242 C. 266 D. 288 Example 3

A. 221 B. 242 C. 266 D. 288 Example 3

Concept

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

Original inequality Isolate the radical. Eliminate the radical. 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

Answer: The solution is 2  x  5. 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

Only the values in the interval 2  x  5 satisfy the inequality. 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. Example 4

A. B. C. D. Example 4

A. B. C. D. Example 4

End of the Lesson