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Foundations & Pre-calculus Math 10
Chapter 3 Notes
REVIEW:
Perfect
square
1
Square Root / Side
length of a square
√1 1
Perfect Cube
4
√4 = 2
8
1
9
27
16
64
Cube Root / Side
length of a Cube
√1 = 1
√8 = 2
125
√ = 6
36
343
√ = 8
64
√ = 9
√81 = 9
100
121
144
√ = 10
√ = 11
√ = 12
√ = 13
√169 = 13
√ = 14
196
225
3375
5
Foundations & Pre-calculus Math 10
Chapter 3 Notes
3.1 Factors and Multiples of Whole Numbers
Define:
1. Factor - ______________________________________________________
2. Prime Number - _______________________________________________
3. Composite Number - ____________________________________________
4. Prime Factorization - ____________________________________________
Ex. #1: Write the prime factorization of 3300.
The prime factors of 3300 are ___________________________
The prime factorization of 3300 is: ______________________________________
Record any divisibility rules that you can recall here:
6
Foundations & Pre-calculus Math 10
Chapter 3 Notes
Ex. #2: Determine the greatest common factor (GCF) of 138 and 198.
The greatest common factor (GCF) is: ____
Ex. #3: Determine the least common multiple (LCM) of 18, 20, and 30.
The least common multiple (LCM) of 18, 20, and 30 is: ____
7
Foundations & Pre-calculus Math 10
Chapter 3 Notes
Ex. #4: Use the skills discussed in examples 1-3 to answer the following.
a) What is the side length of the smallest square that could be tiled with
rectangles that measure 16 cm by 40 cm?
Assume the rectangles cannot be cut. Sketch the square and rectangles.
b) What is the side length of the largest square that could be used to tile a
rectangle that measures 16cm by 40 cm?
Assume that the squares cannot be cut. Sketch the rectangle and squares.
8
Foundations & Pre-calculus Math 10
Chapter 3 Notes
3.2 Perfect Squares, Perfect Cubes, and Their Roots
Ex. #1: Determine the square root of 1296
Group the factors in pairs.
Rearrange the factors in 2 equal
groups.
1296
1296
Notes on Radicals:
√8
√81
√81
9
Foundations & Pre-calculus Math 10
Chapter 3 Notes
Ex. #2: Determine the cube root of 1728.
Group the factors in sets of 3.
Rearrange the factors in 3 equal
groups.
Volume
= 1728
Ex. #3: A cube has volume 4913 cubic inches. What is the surface area of the
cube?
Volume
= 4913
10
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