Chapter 5.8 Radical Equations & Inequalities Standard & Honors Algebra II Mr. Gilbert Chapter 5.8 Radical Equations & Inequalities Standard & Honors 11/29/2018

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Class Work: Warm-up 5.8 (3 min.) Yes –it’s a repeat Work on your own, silently. Write your name on the top of the sheet, turn in when done. Factor Completely (x2-81) = (2x2 +18x +16) = x4-1 = Find the product: (x+1)(2x2-3x+1) = (2n2 -3)(n2+5n -1) = 11/29/2018

Class Work: Warm-up 5.6 (3 min.) Work on your own, silently. Factor Completely, assume no denominator is equal to 0. (x2-81) = (x+9)(x-9) (2x2 +18x +16) = (2)(x+1)(x+8) x4-1 = (x2+1)(x+1)(x-1) Find the product: (x+1)(2x2-3x+1) = 2x3 –x2-2x+1 (2n2 -3)(n2+5n -1) =2n4+10n3-5n2-15n+3 11/29/2018

5-8 Radical Equations & Inequalities Example 1 Solve a Radical Equation (2) Example 2 Extraneous Solution (3) Example 3 Cube Root Equation (3) Example 4 Radical Inequality (4) 11/29/2018 Lesson 8 Contents

Example 1: Solve a Radical Equation (2) Add 1 to each side to isolate the radical. Square each side to eliminate the radical. Find the squares. Add 2 to each side. Replace y with 38. Check Simplify. Answer: The solution checks. The solution is 38. 11/29/2018 Example 8-1a

Solve Answer: 67 11/29/2018 Example 8-1c

Example 2 Extraneous Solution Solve Square each side. Find the squares. Isolate the radical. Divide each side by –4. Square each side. Evaluate the squares. Now let’s check 11/29/2018 Example 8-2a

Example 2 Extraneous Solution cont. Answer: The solution does not check, so there is no real solution. Check Original equation Evaluate the square roots. Replace x with 16. Simplify. 11/29/2018 Example 8-2b

Extraneous Solution Solve . Answer: no real solution 11/29/2018 Example 8-2c

Cube Root Example Solve In order to remove the radical, it this case cube root, you a) must first isolate it and then b) raise it so that it becomes 1 while keeping the equation balanced. Subtract 5 from each side. Cube each side. Evaluate the cubes. Subtract 1 from each side. Divide each side by 3. Now let’s check 11/29/2018 Example 8-3a

Cube Root Example cont. Check Original equation Replace y with –42. Simplify. The cube root of –125 is –5. Add. Answer: The solution is –42. 11/29/2018 Example 8-3b

Cube Root Example Solve Answer: 13 11/29/2018 Example 8-3c

Radical Inequality Solve Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined. 11/29/2018 Example 8-4a

Radical Inequality cont. Now solve . Isolate the radical. Eliminate the radical. Add 6 to each side. Divide each side by 3. Answer: The solution is Now let’s check 11/29/2018 Example 8-4b

Radical Inequality cont. (Since The solution is ) 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. Since is not a real number, the inequality is not satisfied. Since the inequality is satisfied. Since the inequality is not satisfied. Only the values in the interval satisfy the inequality. 11/29/2018 Example 8-4c

Radical Inequality Solve Answer: Answer : -5/2 11/29/2018 Example 8-4d

Earn up to 35 Bonus Points You may earn bonus test points by: Completing 100% correctly the online Self Check Quizzes for all lessons in the last test: 5.1-5.4, 9.1-9.2, 11.7 5% will be added to last test score for each 100% complete lesson. Bonus available until end of day 9/25, mail posted by end of day 9/19 will make the progress report. Use lesson resources in http://www.glencoe.com/sec/math/algebra/algebra2/algebra2_05/ 11/29/2018

Homework Review 11/29/2018

Homework See Syllabus 5.8 p. 266: 13 – 27 odd and 39. 11/29/2018

Homework - Honors See Syllabus 5.8 p. 266: 13 - 39 odd, 41-43 11/29/2018