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4.5E: Exercises

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Practice Makes Perfect

Exercise A: add and subtract radical expressions

In the following exercises, simplify. Assume all variables are greater than or equal to zero so that absolute values are not needed.

  1. a. 8252 b. 53m+23m c. 84m24n

  2. a. 7232 b. 73p+23p c. 53x33x

  3. a. 35+65 b. 93a+33a c. 542z+42z

  4. a. 45+85 b. 3m43m c. n+3n

  5. a. 32a42a+52a b. 543ab343ab243ab

  6. a. 11b511b+311b b. 8411cd+5411cd9411cd

  7. a. 83c+23c93c b. 234pq534pq+434pq

  8. a. 35d+85d115d b. 1132rs932rs+332rs

  9. a. 2775 b. 3403320 c. 12432+234162

  10. a. 7298 b. 324+381 c. 12480234405

  11. a. 48+27 b. 354+3128 c. 645324320

  12. a. 45+80 b. 3813192 c. 52480+734405

  13. a. 72a550a5 b. 9480p464405p4

  14. a. 48b575b5 b. 8364q633125q6

  15. a. 80c720c7 b. 24162r10+4432r10

  16. a. 96d924d9 b. 54243s6+243s6

  17. 3128y2+4y162898y2

  18. 375y2+8y48300y2
Answer

1. a. 32 b. 73m c. 64m

3. a. 95 b. 123a c. 642z

5. a. 42a b. 0

7. a. 3c b. 34pq

9. a. 23 b. 235 c. 342

11. a. 73 b. 732 c. 345

13. a. a22a b. 0

15. a. 2c35c b. 14r242r2

17. 4y2

Exercise B: multiply radical expressions

In the following exercises, simplify.

    1. (23)(318)

    2. (834)(4318)



    3.  
    4.  

    1. (45)(510)

    2. (239)(739)



    3.  
    4.  

    1. (56)(12)

    2. (2418)(49)



    3.  
    4.  

    1. (27)(214)

    2. (348)(546)



    3.  
    4.  

    1. (412z3)(39z)

    2. (533x3)(3318x3)



    3.  
    4.  

    1. (32x3)(718x2)

    2. (6320a2)(2316a3)



    3.  
    4.  

    1. (27z3)(314z8)

    2. (248y2)(2412y3)



    3.  
    4.  

    1. (42k5)(332k6)

    2. (46b3)(348b3)



    3.  
    4.  
Answer

1.

  1. 186

  2. 6439



  3.  
  4.  

3.

  1. 302

  2. 642



  3.  
  4.  

5.

  1. 72z23

  2. 45x232



  3.  
  4.  

7.

  1. 42z52z

  2. 8y46y
Exercise C: use polynomial multiplication to multiply radical expressions

In the following exercises, multiply.

    1. 7(5+27)

    2. 36(4+318)



    3.  
    4.  

    1. 11(8+411)

    2. 33(39+318)



    3.  
    4.  

    1. 11(3+411)

    2. 43(454+418)



    3.  
    4.  

    1. 2(5+92)

    2. 42(412+424)



    3.  
    4.  

  1. (7+3)(93)

  2. (82)(3+2)

    1. (932)(6+42)

    2. (3x3)(3x+1)



    3.  
    4.  

    1. (327)(547)

    2. (3x5)(3x3)



    3.  
    4.  

    1. (1+310)(5210)

    2. (23x+6)(3x+1)



    3.  
    4.  

    1. (725)(4+95)

    2. (33x+2)(3x2)



    3.  
    4.  

  3. (3+10)(3+210)

  4. (11+5)(11+65)

  5. (27511)(47+911)

  6. (46+713)(86313)

    1. (3+5)2

    2. (253)2



    3.  
    4.  

    1. (4+11)2

    2. (325)2



    3.  
    4.  

    1. (96)2

    2. (10+37)2



    3.  
    4.  

    1. (510)2

    2. (8+32)2



    3.  
    4.  

  7. (4+2)(42)

  8. (7+10)(710)

  9. (4+93)(493)

  10. (1+82)(182)

  11. (1255)(12+55)

  12. (943)(9+43)

  13. (33x+2)(33x2)

  14. (34x+3)(34x3)
Answer

1.

  1. 14+57

  2. 436+334



  3.  
  4.  

3.

  1. 44311

  2. 342+454



  3.  
  4.  

5. 60+23

7.

  1. 30+182

  2. 3x223x3



  3.  
  4.  

9.

  1. 54+1310

  2. 23x2+83x+6



  3.  
  4.  

11. 23+330

13. 439277

15.

  1. 14+65

  2. 79203

17.

  1. 87186

  2. 163+607

19. 14

21. 227

23. 19

25. 39x24

Exercise D: mixed practice
  1. 2327+3448

  2. 175k463k4

  3. 56162+316128

  4. 324+381

  5. 12480234405

  6. 841344133413

  7. 512c4327c6

  8. 80a545a5

  9. 35751448

  10. 2139239

  11. 8364q633125q6

  12. 11111011

  13. 321

  14. (46)(18)

  15. (734)(3318)

  16. (412x5)(26x3)

  17. (29)2

  18. (417)(317)

  19. (4+17)(3+17)

  20. (348a2)(412a3)

  21. (632)2

  22. 3(433)

  23. 33(239+318)

  24. (6+3)(6+63)
Answer

1. 53

3. 92

5. 45

7. 10c239c33

9. 23

11. 17q2

13. 37

15. 4239

17. 29

19. 29717

21. 72362

23. 6+332

Exercise E: writing exercises
  1. Explain when a radical expression is in simplest form.
  2. Explain the process for determining whether two radicals are like or unlike. Make sure your answer makes sense for radicals containing both numbers and variables.
    1. Explain why (n)2 is always non-negative, for n0.
    2. Explain why (n)2 is always non-positive, for n0.
  3. Use the binomial square pattern to simplify (3+2)2. Explain all your steps.
Answer

1. Answers will vary

3. Answers will vary

Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has 3 rows and 4 columns. The first row is a header row and it labels each column. The first column header is “I can…”, the second is “Confidently”, the third is “With some help”, and the fourth is “No, I don’t get it”. Under the first column are the phrases “add and subtract radical expressions.”, “ multiply radical expressions”, and “use polynomial multiplication to multiply radical expressions”. The other columns are left blank so that the learner may indicate their mastery level for each topic.
Figure 8.4.14

b. On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?


This page titled 4.5E: Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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