Download Unit C Assignment 1 - ARPDC Learning Portal

Math 10C
Unit 3—Roots and Powers
Outcome
Name:_________________
_
Definition
Demonstrate an understanding of factors of whole numbers by determining the:
 prime factors
 greatest common factor
 least common multiple
 square root
 cube root.
N1
Demonstrate an understanding of irrational numbers by:
N2
N3
• representing, identifying and simplifying irrational numbers
• ordering irrational numbers.
Demonstrate an understanding of powers with integral and rational exponents.
Vocabulary
 Composite number
 Factor tree
 Greatest common factor (GCF)
 Lowest common multiple (LCM)
 Prime Factorization
 Prime factors
 Cube Root
 Perfect cube
 Perfect Square
 Square Root
 Irrational and Rational Numbers
 Entire Radical
 Index
 Mixed radical
 Radicand
 Root
 Base
 Exponent
 Power
 Reciprocal
 Rational Exponents
WS #1: Prime Factorization
1. Tell whether each number is prime, composite, or neither.
1 _________________
29__________________
45 _________________
56__________________
87 _________________
93__________________
15 _________________
44__________________
53 _________________
31__________________
110 ________________
114_________________
2. Find the prime factorization of each number.
a) 42
e) 24
I) 120
b) 17
f) 97
j) 38
c) 102
g) 65
k) 40
d) 81
h) 18
l) 48
3. Find the LCM of the numbers by listing multiples.
a) 3, 4
d) 5, 14
b) 8, 9
e) 8,9, 24
c) 15, 20
f) 12,9
4. Find the LCM of the numbers using prime factorization
a) 30, 10
e) 30, 50
b) 42, 126
f) 75, 105
c) 54, 210
g) 8, 30, 45
d) 36, 54
h) 30, 70,105
5. Find the GCF of the following numbers using prime factorization
a) 18, 20
6. 150, 225
b) 12, 27
e) 36, 54
c) 36, 60, 135
f) 30, 36, 75
d) 45, 75
g) 50, 56, 105
6. Samantha has two pieces of cloth. One piece is 72 inches wide and the other is 90 inches wide. She
wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she
cut the strips?
7. Ben exercises every 3 days and Isabel every 2 days. Ben and Isabel both exercised today. How many
days in the next 30 days will they both exercise on the same day?
8. Use the Prime Factorization method to decide if these numbers are perfect squares and to find the
square roots of those that are perfect squares.
a) 225
d) 484
b) 400
f) 396
c) 360
g) 280
9. A cube has a volume of 512 cm3. Determine the surface area of the cube using prime factorization.
WS # 2: Radicals
1. Determine what category the following numbers fall in. Natural, whole, integer, rational, irrational.
Number
5
Category/ categories
4
3
125
5
8.25
90
2. Use the following radical to answer the next three questions.
5
100
a) What is the index?
b) What is the radicand?
c) What is the value of the radical, rounded to the nearest thousandth if appropriate?
3. Write each of the following as an entire radical.
a) 3 2
d) 5 27
b) 4 3
e) 2 227
c) 2 5
f) 6 8
4. Write each of the following as an entire radical.
a) 4 3 2
d) 5 3 2
b) 7 3 12
e) 14 3 12
c) 2 3 2
5. Write each of the following as a mixed radical.
a)
g) -1 125
5
32
b) - 27
c) 2 50
d) 1
2
e) -3
2
32
24
f) -3 98
3
h)
i)
3
16
40
j) 5 3 24
k) 7 3 375
6. Order these numbers from greatest to least:
,
,
,
,
7. The speed, s, in meters per second, of an aircraft is related to the lift, L, in Newton’s, by the radical
equation s = 0.1 L . When the lift is 1 440 000 N, then the speed, to the nearest meter per second, is
_________m/s.
WS # 3: Negative Exponents
1. Evaluate the following without using a calculator.
a. ( 2) 3
b. 32
c. (6) 0
e.
31
7
g.  4 2
d. 8 1
f. 32
h. 52
2. Simplify
a. y 14  y 6
4 x 
2 2
c.
2x
b. 58  52
d) ( x 3 y 5 )( x 4 y 3 )
3. For each of the following solutions, identify the error that was made. Be specific about what the
error is and determine the correct answer.
a.
( )
4x 3
2
= 4x 3´2
= 4x 6
æ a-2 ö-2 æ 4b3 ö2
÷÷ = çç
÷÷
b. çç
è 4b3 ø
è a2 ø
2 3´2
=4 b
a2´2
= 16b
a4
6
WS #4: Rational Exponents
1. Write each expression in radical form.
1
4
3
a) 7 2
d) 7 3
h) (10m) 2
b)
3
44
3
62
c)
5
23
e)
i)
-1
(5n) 2
1
f) 2 6
6
j) (a) 5
g) (5x)
-5
4
2. Write each expression in exponential form.
a)
( 10 )
b)
( )
c)
4
5
2
( 2)
3
3. Simplify
a.
1
2
9
-4
b) 343 3
3
c) 36 2
3
d)
( 2)
g)
e)
( )
h)
f)
6
4
5
5
( 10 )
6
( m)
4
3
1
( )
3k
5
4. For the following solution, identify the error that was made. Be specific about what the error is and
determine the correct answer.
5
8 4 = 8 54 -2
82
5-8
4
= 84
- 34
=8
4
3
=8
=
( )
3
8
()
= 2
= 16
4
4