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Mathematics LibreTexts

17.3E: Exercises

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Practice Makes Perfect

Exercise SET A: use the product property to simplify radical expressions

In the following exercises, use the Product Property to simplify radical expressions.

  1. 27
  2. 80
  3. 125
  4. 96
  5. 147
  6. 450
  7. 800
  8. 675
    1. 432
    2. 564
    1. 3625
    2. 6128
    1. 564
    2. 3256
    1. 43125
    2. 381
Answer

1. 33

3. 55

5. 73

7. 202

9.

  1. 242
  2. 252

11.

  1. 252
  2. 434
Exercise SET B: use the product property to simplify radical expressions

In the following exercises, simplify using absolute value signs as needed.

    1. y11
    2. 3r5
    3. 4s10
    1. m13
    2. 5u7
    3. 6v11
    1. n21
    2. 3q8
    3. 8n10
    1. r25
    2. 5p8
    3. 4m5
    1. 125r13
    2. 3108x5
    3. 448y6
    1. 80s15
    2. 596a7
    3. 6128b7
    1. 242m23
    2. 4405m10
    3. 5160n8
    1. 175n13
    2. 5512p5
    3. 4324q7
    1. 147m7n11
    2. 348x6y7
    3. 432x5y4
    1. 96r3s3
    2. 380x7y6
    3. 480x8y9
    1. 192q3r7
    2. 354m9n10
    3. 481a9b8
    1. 150m9n3
    2. 381p7q8
    3. 4162c11d12
    1. 3864
    2. 4256
    1. 5486
    2. 664
    1. 532
    2. 81
    1. 38
    2. 416
    1. 5+12
    2. 10242
    1. 8+96
    2. 8804
    1. 1+45
    2. 3+903
    1. 3+125
    2. 15+755
Answer

1.

  1. |y5|y
  2. r3r2
  3. s24s2

3.

  1. n10n
  2. q23q2
  3. |n|8n2

5.

  1. 5r65r
  2. 3x34x2
  3. 2|y|43y2

7.

  1. 11|m11|2m
  2. 3m245m2
  3. 2n55n3

9.

  1. 7|m3n5|3mn
  2. 2x2y236y
  3. 2|xy|42x

11.

  1. 8|qr3|3qr
  2. 3m3n332n
  3. 3a2b24a

13.

  1. 634
  2. not real

15.

  1. 2
  2. not real

17.

  1. 5+23
  2. 56

19.

  1. 1+35
  2. 1+10
Exercise Set C: use the quotient property to simplify radical expressions

In the following exercises, use the Quotient Property to simplify square roots.

    1. 4580
    2. 3827
    3. 4181
    1. 7298
    2. 32481
    3. 4696
    1. 10036
    2. 381375
    3. 41256
    1. 12116
    2. 316250
    3. 432162
    1. x10x6
    2. 3p11p2
    3. 4q17q13
    1. p20p10
    2. 5d12d7
    3. 8m12m4
    1. y4y8
    2. 5u21u11
    3. 6v30v12
    1. q8q14
    2. 3r14r5
    3. 4c21c9
  1. 96x7121
  2. 108y449
  3. 300m564
  4. 125n7169
  5. 98r5100
  6. 180s10144
  7. 28q6225
  8. 150r3256
    1. 75r9s8
    2. 354a8b3
    3. 464c5d4
    1. 72x5y6
    2. 596r11s5
    3. 6128u7v12
    1. 28p7q2
    2. 381s8t3
    3. 464p15q12
    1. 45r3s10
    2. 3625u10v3
    3. 4729c21d8
    1. 32x5y318x3y
    2. 35x6y940x5y3
    3. 45a8b680a3b2
    1. 75r6s848rs4
    2. 324x8y481x2y
    3. 432m9n2162mn2
    1. 27p2q108p4q3
    2. 316c5d7250c2d2
    3. 62m9n7128m3n
    1. 50r5s2128r2s6
    2. 324m9n7375m4n
    3. 481m2n8256m1n2
    1. 45p95q2
    2. 46442
    3. 5128x852x2
    1. 80q55q
    2. 362535
    3. 480m745m
    1. 50m72m
    2. 312502
    3. 4486y92y3
    1. 72n112n
    2. 31626
    3. 4160r105r3
Answer

1.

  1. 34
  2. 23
  3. 13

3.

  1. 53
  2. 35
  3. 14

5.

  1. x2
  2. p3
  3. |q|

7.

  1. 1y2
  2. u2
  3. |v3|

9. 4|x3|6x11

11. 10m23m8

13. 7r22r10

15. 2|q3|715

17.

  1. 5r43rs4
  2. 3a232a2|b|
  3. 2|c|44c|d|

19.

  1. 2|p3|7p|q|
  2. 3s233s2t
  3. 2|p3|44p3|q3|

21.

  1. 4|xy|3
  2. y23x2
  3. |ab|4a4

23.

  1. 12|pq|
  2. 2cd52d25
  3. |mn|622

25.

  1. 3p4p|q|
  2. 242
  3. 2x52x

27.

  1. 5|m3|
  2. 535
  3. 3|y|43y2
Exercise SET D: writing exercises
  1. Explain why x4=x2. Then explain why x16=x8.
  2. Explain why 7+9 is not equal to 7+9.
  3. Explain how you know that 5x10=x2.
  4. Explain why 464 is not a real number but 364 is.
Answer

1. Answers may vary

3. Answers may 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 “use the product property to simplify radical expressions” and “use the quotient property to simplify radical expressions”. The other columns are left blank so that the learner may indicate their mastery level for each topic.
Figure 8.2.1

b. After reviewing this checklist, what will you do to become confident for all objectives?


This page titled 17.3E: Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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