1. Chapter 5.8 Radical Equations & Inequalities Standard & Honors
Algebra II Mr. Gilbert
Chapter 5.8 Radical Equations & Inequalities
Standard & Honors
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2. Agenda Warm-up (next slide) Review Homework Return Class work
Check your answers
Review Homework
Return Class work
Bonus points
Lesson
Homework
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3. 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) =
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4. 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
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5. 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)
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Lesson 8 Contents

6. 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.
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Example 8-1a

7. Solve
Answer: 67
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Example 8-1c

8. 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
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Example 8-2a

9. 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.
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Example 8-2b

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

11. 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
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Example 8-3a

12. 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.
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Example 8-3b

13. Cube Root Example
Solve
Answer: 13
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Example 8-3c

14. 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.
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Example 8-4a

15. 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
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Example 8-4b

16. 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.
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Example 8-4c

17. Radical Inequality
Solve
Answer:
Answer : -5/2
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Example 8-4d

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19. Homework Review
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20. Homework
See Syllabus 5.8
p. 266: 13 – 27 odd and 39.
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21. Homework - Honors See Syllabus 5.8 p. 266: 13 - 39 odd, 41-43
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