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Lesson Menu Five-Minute Check (over Lesson 7–6) 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 Key Concept: Solving Radical Inequalities Example 4:Solve a Radical Inequality

Over Lesson 7–6 A.A B.B C.C D.D 5-Minute Check 1 A. B. C. D.

Over Lesson 7–6 A.A B.B C.C D.D 5-Minute Check 2 A.12 B.8 C.4 D.2

Over Lesson 7–6 A.A B.B C.C D.D 5-Minute Check 3 A. B. C. D.

Over Lesson 7–6 A.A B.B C.C D.D 5-Minute Check 4 A.2w 2 B.2w C.w 2 D.

Over Lesson 7–6 A.A B.B C.C D.D 5-Minute Check 5 A. B. C.5 D.10

Over Lesson 7–6 A.A B.B C.C D.D 5-Minute Check 6 A.82.6 kcal/day B kcal/day C kcal/day D kcal/day 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.

Then/Now You solved polynomial equations. (Lesson 6–5) Solve equations containing radicals. Solve inequalities containing radicals.

Vocabulary radical equation extraneous solution radical inequality

Concept

Example 1 Solve Radical Equations A. Solve. Add 2 to each side. Find the squares. Square each side to eliminate the radical. Add 1 to each side to isolate the radical. Original equation

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

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

Example 1 Solve Radical Equations Square each side. Evaluate the squares. Replace x with 16. Simplify. Original equation Check Evaluate the square roots. Answer: The solution does not check, so there is no real solution. 

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

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

Example 2 Solve a Cube Root Equation Original equation Subtract 5 from each side. Cube each side. Evaluate the cubes. 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.

Example 2 Solve a Cube Root Equation Answer: The solution is –42. Subtract 1 from each side. Divide each side by 3. Original equation Replace y with –42. Simplify. The cube root of –125 is –5. Add. Check

A.A B.B C.C D.D Example 2 A.–14 B.4 C.13 D.26

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

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

Concept

Example 4 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63x6 x2x2

Example 4 Solve a Radical Inequality Answer: The solution is 2  x  5. Original inequality Isolate the radical. Eliminate the radical. Add 6 to each side. Divide each side by 3.

Example 4 Solve a Radical Inequality Check Only the values in the interval 2  x  5 satisfy the inequality. 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.

A.A B.B C.C D.D Example 4 A. B. C. D.

End of the Lesson