Name: ______________________
Math 860 – 7.1, 7.2
1. Evaluate each square root, if possible, without using a calculator:
a.
 81
1
16
0.25
c.
2. Simplify each expression. Assume that all variables are unrestricted and use absolute value
symbols when necessary.
b. 
a.
4x 2
b.
9y4
b 2  14b  49
c.
3. Use a calculator to find the following square root. Round your answer to 4 decimals: 13
4. Let g ( x)  x  4 . Find each function value:
a. f (8)
b. f (29)
5. Complete the table and the graph of the function. Find the domain and range of the function:
f ( x)  x  2
f (x )
x
0
1
4
9
16
6. Simplify each cube root:
8
a. 3
27
1
3
 216a 3
b.
7. Simplify each radical expression. Assume all variables are unrestricted:
a.
5
32b 5
b.  4 81
8. Evaluate each expression:
1
a. 125
3
1
1 2
b.  
4
9. Simplify each expression, if possible. Assume that the variables can be any real number, and
use absolute value symbols when necessary.
a 4 
 27n 9 
1
a.
4
1
3
b.
10. Evaluate each expression:
a. 36
b.
3
2
 125 3
2
2
 27  3
 . All variables represent positive real numbers (so you
11. Simplify the expression:  
 64 y 6 


don’t need to use absolute value symbols here).
12. Change the following radical into an exponential expression (you do NOT have to simplify):
7 9 p 2q

13. Change the exponential expression into a radical (you do NOT have to simplify): x 3  y 3
14. Simplify each expression. Assume all variables represent positive real numbers:

a. 49
1

1
3
2
 
3
b.  81c 4
15. Simplify each expression. Write the answers without negative exponents. All variables
represent positive real numbers.
a.
a b 
1
2
4
b.
b 5b
1
1
3
3
2
2
5
3
b 5
16. Use rational exponents to simplify each radical:
a. 6 p 3
b. 4 x
2