Download Number Review_1

Math 10C
Real Numbers: Review
Number Unit Review
If you had trouble with Prime Factorization, try these questions:
1. Write the prime factorization of:
a) 728
b) 4275
2. Use prime factorization to determine if 1728 is a perfect square, perfect cube, neither, or
both.
If you had trouble with Greatest Common Factor, try these questions:
3. Find the GCF of:
a) 180 and 468
b) 90, 75, and 315
If you had trouble with Least Common Multiple, try these questions:
4. Find the LCM of:
a) 24 and 28
b) 135, 150, and 225
Math 10C
Real Numbers: Review
If you had trouble with Number Systems, try these questions:
5. List all the number systems that the following numbers belong to:
9
a) 
b) 4 17
c) 0
d)
7
3
125
6. True or false?
a) All negative numbers are integers.
b) All repeating decimals are rational numbers.
c) Every natural number is also an integer.
d) A number can be both an integer and irrational.
If you had trouble with Evaluating and Ordering Radicals, try these questions:
7. Evaluate the following radicals to the nearest hundredth.
a)
5
168
b) 4 0.89
c)
36  3 20
d)
10  4 8
3
8. Put the radicals from #7 in order from least to greatest.
If you had trouble with Equivalent Radicals, try these questions:
9. Write the following radicals as mixed radicals in simplest form:
a) 396
b) 375
c) 3 128
10. Find the length of the missing side of this triangle, and write it as a mixed radical in
simplest form.
3 cm
13 cm
Math 10C
Real Numbers: Review
11. A square has area 252 mm2. Write the length of one side as a mixed radical in simplest
form.
12. Write the following as entire radicals:
a) 8 3
b) 43 5
c) 24 11
13. Explain how you use the index of the radical to write a mixed radical as an entire radical.
If you had trouble with Exponent Laws, try these questions:
14. Simplify the following using exponent laws:

a)  7a  2a

5 2
 10m3n7 

c) 
2 4 
 5m n 
18 xy8
b)
16 xy3
4
5
d)  
3
If you had trouble with Negative Exponents, try these questions:
15. Evaluate:
a) 7 4
 11 
b)  
3
2
c)
11
32
3
Math 10C
Real Numbers: Review
16. Simplify each power and write with positive exponents:
 
a) n
xy 
5 3
4b
b)
12b 5
4 6
c)
x 9 y 2
If you had trouble with Rational Exponents, try these questions:
17. Julia is a veterinarian. She gave a horse 40 g of a particular drug at 10:00 a.m. Now it is
3:00 p.m., and she needs to determine how much of the drug is remaining in the horse’s
t
 1 4
bloodstream. She can use the formula A  I   , where I is initial amount of the drug
2
that was given to the horse, and t is the number of hours that have passed since the drug
was given. To the nearest tenth, how much of the drug is still in the horse’s bloodstream
at 3:00 p.m.?
18. Write as a radical and then evaluate:
3
a) 216
 25  2
b)  
 49 
1
3
c) 16
 34
19. Write each power as an equivalent radical:
a) m
7
3
 6x
b) 2 x
3
2
 a8 
c)  3 
a 
 14
d) 27n 5 3
2
Math 10C
Real Numbers: Review
20. Write each radical as an equivalent power with positive exponents:
a)
m12
7
b)
9
Answer Key:
1. a) 728  23  7  13
2. perfect cube
3. a) 36
b) 15
4. a) 168
b) 1350
5. a) Q
b) Q
6. a) False
b) True
7. a) 2.79
b) 3.77
8. c, d, a, b
9. a) 6 11
b) 5 15
10. 4 10 cm
11. 6 7 mm
b3
y5  4 y
c)
b) 4275  32  52 19
c) W, I, Q
c) True
c) 2.21
d) N, W, I, Q
d) False
d) 2.77
c) 43 2
12. a) 192
b) 3 320
c) 4 176
13. The index is the number you use as the power of the coefficient.
125
9 y5
12
14. a) 196a
b)
c) 16m4 n12
d)
27
8
1
9
15. a)
b)
c) 99
2401
121
1
1
y 17
16. a) 24
b) 4
c) 6
3b
n
x
17. 16.8 g
3
3
18. a)
19. a)
3
3
216  6
m7
20. a) m
12
7
 1 
 or
c)  4

16


 25  125
 
b) 
 343
49


b) 12 x 5
b) b
1
6
c)
1
4
c) y
a
11
4
5
1
 16 
4
d) 9 3 n10
3

1
8