Name
Class
6-2
Date
Practice
Form K
Multiplying and Dividing Radical Expressions
Multiply, if possible. Then simplify. To start, identify the index of each radical.
1.
3
43 6
5 8
2.
3.
3
64 9
index of both radicals is 3
3
46
Simplify. Assume all variables are positive. To start, change the radicand to factors with
the necessary exponent.
4.
3
27x 6
48x3 y 4
5.
6.
5
128x 2 y 25
 3 33  ( x 2 )3
Multiply and simplify. Assume all variables are positive.
12  3
7.
8.
4
7 x6  4 32 x 2
9. 2 3 6 x 4 y  3 3 9 x5 y 2
Simplify each expression. Assume all variables are positive.
10.
3
4  3 80
11. 5 2 xy 6  2 2 x3 y
13. Error Analysis Your classmate simplified
12.
5

5  15
5 x3  3 5 xy 2 to 5x2y. What mistake did
she make? What is the correct answer?
14. A square rug has sides measuring
3
16 ft by 3 16 ft. What is the area of the rug?
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
Name
Class
6-2
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.
36 x 6
15.
4
16.
4
9 x4

405 x8 y 2
3
17.
5 x3 y 2
75 x 7 y 2
25 x 4
4
36 x 6
9 x4
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 denominator.
26
3
18.

3
19.
3
x
2
20.
7 x4 y
5 xy
26 3

3
3
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 = 16t2 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 in
terms of a?
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16