Name Class Date Practice
Form K
Multiplying and Dividing Radical Expressions
Multiply, if possible. Then simplify. To start, identify the index of each radical.
3
1. 14
# 16
3
index of both radicals is 3
3
1
4
#6
2. 15
# 18
3
3. 16
# 19
4
Simplify. Assume all variables are positive. To start, change the radicand to
factors with the necessary exponent.
3
4. 227x 6
3 3
=2
3
# (x2)3
5
5. 248x 3y 4
6. 2128x 2y 25
Multiply and simplify. Assume all variables are positive.
7. 112
# 13
4
8. 27x 6
# 232x2
4
3
9. 2 26x 4y
# 3 29x5y2
3
Simplify each expression. Assume all variables are positive.
3
10. 14
# 180
3
11. 5 22xy 6
# 2 22x3y
13. Error Analysis Your classmate simplified 25x 3
did she make? What is the correct answer?
12. 15 1 15 + 115 2
# 25xy2 to 5x2y. What mistake
3
3
3
14. A square rug has sides measuring 1
16 ft by 1
16 ft. What is the area of the rug?
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date Practice (continued)
Form K
Multiplying and Dividing Radical Expressions
Divide and simplify. Assume all variables are positive. To start, write the
quotient of roots as a root of a quotient.
15.
236x6
19x4
4
16.
6
= 5 36x4
9x
2405x8y 2
4
15x3y 2
3
17.
275x7y 2
3
125x4
Rationalize the denominator of each quotient. Assume all variables are positive.
To start, multiply the numerator and denominator by the appropriate radical
expression to eliminate the radical.
18.
126
13
=
126
13
19.
13
# 13
3
1
x
3
12
20.
27x4y
15xy
21. Einstein’s famous formula E = mc2 relates energy E, mass m, and the speed of
light c. Solve the formula for c. Rationalize the denominator.
22. The formula h = 16t 2 is used to measure the time t it takes for an object to free fall from
height h. If an object falls from a height of h = 18a5 ft, how long did it take for the object
to fall in terms of a?
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date Practice
Form G
Multiplying and Dividing Radical Expressions
Multiply, if possible. Then simplify.
# 125
4. 245 # 275
# 136
5. 118 # 150
1. 14
3
# 1 27
6. 1 -16 # 14
2. 181
3
3. 13
3
3
3
Simplify. Assume that all variables are positive.
3
7. 236x 3
8. 2125y 2z 4
3
10. 2
-16a12
3
13. 2216x 4y 3
9. 218k 6
11. 2x2y 10z
4
12. 2
256s7t 12
14. 275r 3
15. 2625u5v 8
4
Multiply and simplify. Assume that all variables are positive.
# 16
19. 412x # 3 18x
22. 212x 2y # 23xy 4
16. 14
17. 29x 2
# 29y5
# 14xy
23. 2-9x 2y 4 # 212xy
20. 1xy
3
3
3
18. 250x 2z 5
28.
31.
175
13
16x
13x
2(2x)2
1(5y)4
26.
29.
163xy 3
17y
3
14x2
3
1x
3
32.
218y 2
3
112y
3
# 3 1y
24. 7 23y 2 # 2 26x 3y
21. 9 12
Divide and simplify. Assume that all variables are positive.
25.
# 215y3z
27.
154x5y 3
12x2y
3
4
30. 2243k
7
3k
33. 5 162a
6a3
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date Practice (continued)
Form G
Multiplying and Dividing Radical Expressions
Rationalize the denominator of each expression. Assume that all variables are positive.
34.
1y
15
35.
9x
37. 5 2
40.
4
12x
4
13x2
38.
3
118x2y
12y 3
36.
1xy
17xy 2
3
1 4x2
3 x2
39. 53y
13x
x
41. 5 8y
3 3a
42. 5 2
4b c
43. What is the area of a rectangle with length 1175 in. and width 163 in.?
44. The area of a rectangle is 30 m2. If the length is 175 m, what is the width?
2
45. The volume of a right circular cone is V = 1
3pr h, where r is the radius of the base and h
is the height of the cone. Solve the formula for r. Rationalize the denominator.
3
46. The volume of a sphere of radius r isV = 4
3pr .
a. Use the formula to find r in terms of V. Rationalize the denominator.
b. Use your answer to part (a) to find the radius of a sphere with volume
100 cubic inches. Round to the nearest hundredth.
Simplify each expression. Rationalize all denominators. Assume that all
variables are positive.
47. 114
6 12x
50.
513
# 121
3
48. 1150
8
51. 3 2
12x
# 120
3
(
49. 13 112 - 16
3
5 1xy 4
52. 3
125xy 2
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
)