7.2 Multiplying & Dividing Radical Expressions
36. a. Simplify
2 3
75
Name:
by multiplying the numerator and denominator by
b. Simplify the expression in (a) by multiplying by
c. Explain how you would simplify
2 3
98
3 instead of
75 .
75 .
.
Simplify each expression. Rationalize all denominators. Assume that all variables are positive.
5  40
37.
40. 5 2 xy 6  2 2 x 3 y
5 ( 5  15 )
43.
5x 4
46.
2
2x y
49.
10
3
5x 2
3
38.
3
41.
44.
47.
3
4  3 80
39.
2 ( 50  7)
42. 3(5  21)
2x  3 4  3 2x 2
45.
5 2
3 7x
3
50.
3
14
7x 2 y
48.
51.
x 5 y 5  3 2x 7 y 6
3
3x 2  3 x 2  3 9 x 3
1
3
9x
3 11x 3 y
 2 12 x 4 y
52.  2(3 32  3 54 )
53.
3 5
5
3 2
54.
55. The circular velocity v, in miles per hour, of a satellite orbiting Earth is given by the formula v 
8
1.24  1012
,
r
where r is the distance in miles from the satellite to the center of Earth. How much greater is the velocity of a
satellite orbiting at an altitude of 100 mi than one orbiting at an altitude of 200 mi? (The radius of Earth is 3950 mi.)
56. A rectangular shelf is
440 cm by
20 cm. Find its area.
57. Explain the error in this simplification of radical expressions.
 2   8   2(8)  16  4
58. A freely falling object hit the ground in
59. Does
18a 5 seconds. It fell h feet. Use the formula h  16t 2 to find h in terms of a.
x 3  3 x 2 for all, some, or no values of x? Explain.
Simplify each expression. Rationalize all denominators. Assume that all variables are positive.
16 x 4 y 4
61.
64.
3
x 1 y 2
62.
3
65.
5
64 x 6 y 12
x 4 y
3
63.
66.
6
8000
y 3
x 4