Mod 3 practice problems
1. Name the precise set of numbers to which each number belongs :
Natural, Whole, Integer , Rational, Irrational, Real or none of these.
a)  144
____________
b) 5 ____________
c)
d) 4.2
____________
e) 7.1213….. __________
f)
3
27 __________
10 ____________
2. What is a prime number and give an example?
3. What is the prime factorization of 36?
4. What is the lowest common multiple of 16 and 40?
5.
Arrange the following radicals in order on the number line:
5 5 , 2 6, 3 7, 4 10, 2 12
6.
Evaluate. Round to the nearest hundredth as needed:
a)
b)
c)
3
 0.01
64  3 27
_______________________
0.02359
_______________________
3
( )
74
_______________________
7.
d3
is used to describe violent storms, where D is the diameter of the
830
storm in kilometres, and t is the number of hours the storm will last. If a storm has a diameter
of 37 km, how long will it last? Round to the nearest tenth of an hour.
The formula T =
3
_______________________
8.
9.
Express as a mixed radical.
3
a)
63
____________
b)
108
____________
c)
135
____________
d)
175
____________
e)
96
____________
f) 2 3 24
____________
Express as an entire radical.
a) 4 7
____________
b) 3 3 2
____________
c) 3 3125
____________
d) 5 6
____________
e) 5 3 2
____________
f) 3 4 2
____________
10. Simplify:
48  27  12
_______________________
b) 9 2  2 2  4 2
_______________________
300  4 12
_______________________
a)
c)
d) 4 200  5 2
_______________________
e) 5 3 7  4 3 7
_______________________
f)
3
375  3 24
_______________________
11. Evaluate:
a)
2
3 3
4 
d) 13x
0
5
_________
_________
b) (7x)0
1
e)  
9
 81  4
c)  
 16 
_________
_________
2.5
_________
f) (2)4
_________
g)

125

6
4
_________
j) 42
h) 32
______________
1
i) 37 ´ 37
_________
k) 32  33
_________
______________
12. Express each power as a radical.
a) 4
d) x
2
3
1
2
5
4
_________
c) 81
_________
f) (- 2)3
_________
m 
_________
c)
7
_________
8
_________
f)
_________
b) 7
_________
 1 9
e)  
9
_________
1
m
n
4
13. Express each radical as a power.
a)
m3
_________
b)
x8
_________
e)
5 3
53
5
d)
3
n
y3
_________
14. Simplify. Answers must contain positive exponents only.
2
a) (2x y )(5x y )
______________
 2 x3 
b)  2 
 3y 
c) (x2y3)2
______________
d) 3m2  4m6
e) (y3)0
______________
f)
______________
h)
3 3
 m3 
g)  2 
n 
4 2
5
i) (2x4y2)3
______________
3ab4 12a5b

2a 3b 2 15ab
10x - 2
- 2x - 3
______________
______________
______________
______________
15.
Evaluate. Exact answers where possible, otherwise, round to the nearest hundredth.
 0.01
4
  
a)  3  3  _________
  
1
6
5
6
6
b)
36

16. Barb incorrectly simplified 27x4
answer?

 64  3
_________ c)  1 
 2 
 6 
2
2
3
1
2
_________
8
as 18x 3 . What error did she make? What is the correct