Page 514
Worked out solutions
1. IS the radical expression in the simplest form? Explain.
3
2 is in simplest form because the radicand cannot be simplified, nor is there
a.
2
a radicand in the denominator
3
b.
is not in simplest form because there is a square root in the denominator
16
that can be simplified
c. 5 40 is not in simplest form because the radicand has a perfect square factor
2. Explain how to use the product property of radicals to simplify
Multiply the two together to get 45 .
Factor using perfect squares 9  5
Simplify to 3  5
3. Explain how to use the quotient property to simplify
3  15
4
25
4
25
Both the numerator and denominator are perfect squares and may be simplified to
2
5
MATCH THE RADICAL EXPRESSION WITH ITS SIMPLIFIED FORM
Use the quotient property to rewrite as
4.
5.
6.
7.
32  16  2  4 2
54  9  6  3 6
486  81  6  9 6
8  4 2 2 2
8. Find the maximum speed of a sailboat with a 25-foot water line using the formula
From example 3.
16
16
16(25)
16 25 4  5 20
s2 
x
s 2  25 s 



substitute 25 for x
9
9
9
3
3
9
9. The error is that they chose the wrong factors of 50. The square root of 5 and the
square root of 10 are not perfect squares. They should have used the square roots of
25 and 2.
Simplify the expression
10. 44  4  11  2 11
26. 2 
10
 2 5
2
27. 3 
9
 3 3
3
28. 8 
13
13
13
 8
 8
9
3
9
29. 3 
8
3 8 3 4 2 6 2 3 2




64
8
8
4
64
30. 4 
16
 4 4  42  8
4
1
1
1
12 
4  3  2 3  3
18.
2
2
2
31. 3 
3
3 3 3 3


16
4
16
1
1
1
54 
9  6  3 6  6
3
3
3
32. 5 
6
5 3
2
33. 8 
20
8 5
4
11.
27  9  3  3 3
12.
48  16  3  4 3
13.
75  25  3  5 3
14.
90  9  10  3 10
15. 125  25  5  5 5
16.
17.
19.
200  100  2  10 2
80  16  5  4 5
20.
2  8  16  4
21.
6  8  48  16  3  4 3
22.
7

9
23.
11
11
11


16
4
16
24. 2 
7
7

3
9
5
5
5
 2
 2 
 5
4
2
4
5
5
5
 18 
 18 
2 5
25. 18 
81
9
81
34.
32
16 2 4 2


5
5
25
35.
27

36
36.
49 7

2
4
37.
36 6
 2
3
9
9 3 3 3
3


6
6
2
38.
39.
44.
9
3

49 7
45.  2 27  3  2 81  2  9  18
48
16 3 4 3


9
9
81
46.
40.
9  4 25  3  4  5  60
7
64 8
 2
16 4
47.  4 
41.
120

4
4 30 2 30

 30
2
2
48.
42.
1
1
1
32  2 
64   8  4
2
2
2
18
 7  6  42
3
81
9
3
 4   4   6
6
2
36
10 16
 16 2  4 2
5
49.  2 20   2 4 5   2  2 5   4 5   2 5
10
10
10
5
100
43. 3 63  4  3 9 7  2  3  3  2 7  18 7