b) Example: One extraneous root can occur when the squaring of both sides results in a quadratic expression MHR • Pre-Calculus 11 Solutions Chapter 5 Page
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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
472
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) 214b) 375 325(3) 15 3 c) 33
3 3 3
24 8(3)
2(3) 23d)
32 2 2
()( )cd c c d cd cSection 5.1 Page 278 Question 3
a) 42 23 8 3 4(2)( )( )
62,mmmm 2 Rm b)
533233
2 324 2 (3)( )( )
23, Rqq
qq q q c)5565 5 55
52 160 2 2 (5)( )( )( )
45,,Rsts t t
st t s tMHR •
Pre-Calculus 11 Solutions Chapter 5 Page 1 of 66Section 5.1 Page 279 Question 4
Mixed Radical Form Entire Radical Form
35n2 22
35 (3)(5)
45 , 0 or 45 , 0nn
nn nn 3333432 2( 6) 6 2
3 4323 172aa
3 3 3 3 3 3 2
117(22
1 (7 )87,08aa
aa a a a a 7)34 333
3128 4 (2) ( )
42xxxxx 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 58 125 8 25(5)
40 5b) For 8
8112z and
448 7z, express both radicals in terms of 7.
884
8 112 8 16(7)
32 7zz
z 4248 7 48 7zz
c) For 2435w and
104381w, express the second radical in terms of
2 w. 2435w
10 4 8 244
224
381 33( )( )
9ww ww w d) For 362 and
36 54, express the second radical in terms of
3 2. 3 62334
3
654 63(2)
18 2Section 5.1 Page 279 Question 6
MHR •
Pre-Calculus 11 Solutions Chapter 5 Page 2 of 66 a) 36 9(6) 5410 100 7 2 49(2)
98The numbers from least to greatest are 36, 72, and 10. b) 23 4(3) 12
416 3 2 9(2)
18772422
14The numbers from least to greatest are 32, -4,
722, and23. c) 3 21
33
3
32 27(2)
5433
3
2.8 2.8
21.952
333
25 8(5)
40The numbers from least to greatest are
321, 2.8,
32 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) 44 411 1 5 11 15 4 11 14
d)951 2610106 621223 3
0Section 5.1 Page 279 Question 9
a) 375 27 325(3) 9(3)15 3 3 3
12 3MHR •
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 67c) 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) 33333 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) 333268