[PDF] Chapter 5 Radical Expressions and Equations





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Chapter 5 Radical Expressions and Equations

Section 5.1 Working With Radicals

Section 5.1 Page 278 Question 1

Mixed Radical Form Entire Radical Form

47
2

4 7 4 (7) 112

50 25(2) 5 2 50

11 8 2

11 8 11 (8) 968

200 100(2) 10 2 200

Section 5.1 Page 278 Question 2

a) 56 4(14) 214
b) 375 325(3) 15 3 c) 33
3 3 3

24 8(3)

2(3) 23
d)

32 2 2

()( )cd c c d cd c

Section 5.1 Page 278 Question 3

a) 42 2

3 8 3 4(2)( )( )

62,mm
mm 2 Rm b)

533233

2 3

24 2 (3)( )( )

23, Rqq

qq q q c)

5565 5 55

5

2 160 2 2 (5)( )( )( )

45,,Rsts t t

st t s t

MHR •

Pre-Calculus 11 Solutions Chapter 5 Page 1 of 66

Section 5.1 Page 279 Question 4

Mixed Radical Form Entire Radical Form

35n
2 22

35 (3)(5)

45 , 0 or 45 , 0nn

nn nn 3333

432 2( 6) 6 2

3 432
3 172aa
3 3 3 3 3 3 2

117(22

1 (7 )8

7,08aa

aa a a a a 7)

34 333

3

128 4 (2) ( )

42xxx
xx 34
128x

Section 5.1 Page 279 Question 5

a) For 15 5 and 8 125, express the second radical in terms of 5. 15 5

8 125 8 25(5)

40 5
b) For 8

8112z and

4

48 7z, express both radicals in terms of 7.

88
4

8 112 8 16(7)

32 7zz

z 42

48 7 48 7zz

c) For 24

35w and

104

381w, express the second radical in terms of

2 w. 24
35w

10 4 8 244

22
4

381 33( )( )

9ww ww w d) For 3

62 and

3

6 54, express the second radical in terms of

3 2. 3 62
334
3

654 63(2)

18 2

Section 5.1 Page 279 Question 6

MHR •

Pre-Calculus 11 Solutions Chapter 5 Page 2 of 66 a) 36 9(6) 54

10 100 7 2 49(2)

98
The numbers from least to greatest are 36, 72, and 10. b) 23 4(3) 12

416 3 2 9(2)

18

772422

14

The numbers from least to greatest are 32, -4,

722
, and23. c) 3 21
33
3

32 27(2)

54
33
3

2.8 2.8

21.952

33
3

25 8(5)

40

The numbers from least to greatest are

3

21, 2.8,

3

2 5, and

3 32.

Section 5.1 Page 279 Question 7

2 3 3.464... -4 3 2 4.242...

72 3.741...2

The numbers from least to greatest are 32, -4,

722
, and23.

Section 5.1 Page 279 Question 8

a) 5954545 b) 1.4 2 9 2 7 10.4 2 7 c) 44 4

11 1 5 11 15 4 11 14

d)

951 2610106 621223 3

0

Section 5.1 Page 279 Question 9

a) 375 27 325(3) 9(3)

15 3 3 3

12 3

MHR •

Pre-Calculus 11 Solutions Chapter 5 Page 3 of 66 b) 2 18 9 7 63 2 9(2) 9 7 9(7)

62 97 37

62 67
c) 8 45 5.1 80 17.4 8 9(5) 16(5) 22.5

24 5 4 5 22.5

28 5 22.5

d) 3333
3 3 3

125(3)2375 281 4 99 5 11 27(3)4 9(11) 5 1134 3 4

532 3 12 11 5 114

13 37114

Section 5.1 Page 279 Question 10

a) 333
268

8, 0aaa

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