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Name _____________________________________________
Algebra II & Trigonometry
A2.A.13
Date _____________________________________
Roots and Radicals
Simplify radical expressions
Evaluate each given expression by finding the indicated root(s). Let each variable represent a positive number.
1. 9
2.  9
3.  9
4. 225
5.  121
9.
13.
3
64
4y 4
6.
n2
7.
10.
5
11.  400
64
14.  b 6
0.25
15. 
4
49
Find, in each case, the smallest value of x for which the radical represents a real number.
17. x  8
18. x  3
19. 2x  5
8.
64
12.
16. 
20.
81x 2
a2
36
3x  10
21. True or False: The principal square root of a positive number is positive.
22. True or False: If n is an even counting number, then
n
kn  k
Solve each equation for the variable when the replacement set is the set of real numbers.
23. x 2  16
24. y 2  169
25. w 2  5
26. 3y 2  75
27. n 2  4  0
28. x 2  1  0
29. y 3  1  0
30. 8b 3  1
31. n 4  81  0