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Math 90: Unit 1 – Square Roots of Perfect Squares
1.1 Square Roots of Perfect Squares
A fraction in simplest form is a perfect square if it can be
written as a product of two equal fractions.
i.e. 16/25, 49/64, etc
A decimal is a perfect square when it can be written as a
fraction that is a perfect square.
i.e. 0.81, 2.25, etc
Examples:
Determining a Perfect Square Given its Square Root
1. Calculate the number whose square root is:
a)
2
5
b) 1.3
Identifying Fractions that are Perfect Squares
2. Is each fraction a perfect square? Explain your reasoning.
a)
8
18
b)
3
4
c)
4
25
Identifying Decimals that are Perfect Squares
3. Is each decimal a perfect square?
a) 0.125
b) 1.44
c) 0.64
d) 0.0144
Assignment: pages 11-13, #1 – 16 all
Journal: AFQ 13, Reflect
1.2 Square Roots of Non-Perfect Squares
Numbers that can not be written as a product of two equal
numbers are non-perfect squares.
The square roots of all non-perfect squares are irrational
numbers and cannot be expressed as the ratio of two
integers.
Consequently, when expressed as a decimal, the square
root of a non-perfect square is a never ending and never
repeating number.
Examples:
Estimating a Square Root of a Fraction
1. Determine an approximate value of each square root:
a)
8
5
b)
c)
3
10
3
7
Finding a Number with a Square Root between Two
Given Numbers
2. Identify a decimal that has a square root between 8 and 9.
Check your answer.
Applying the Pythagorean Theorem
3. A ramp was constructed to load a truck. The ramp is 9
feet long and the horizontal distance from the bottom of the
ramp to the truck is 7 feet.
a) Estimate the vertical height of the ramp to the nearest
tenth of a meter
b) Use a calculator to check the answer
Assignment: pages 16 – 18, #1 – 13;
Journal: AFQ 14 and Reflect
Mid-Unit Review: page 21, #1-11
What is surface area?
The measure of how much exposed area an object has.
Surface area is expressed in square units.
If an object has flat faces, its surface area can be calculated by
adding together the areas of its exposed faces.
Formulas:
Area of a square or rectangle = (length) (width)
Area of a triangle = ½ (base) (height)
Area of a circle =
 r2
Circumference of a circle =
diameter
2 r or  d (r = radius and d =
Activity:
With a partner, find the surface area of the following objects.
For each object:
a) Draw a diagram
b) Measure the surfaces and find the area of each surface; label
your diagram
c) Find the sum of the areas in part b (the surface area).
Measure to the nearest millimeter
1. Smarties box
2. Toblerone chocolate bar
3. Rolo chocolate bar
1.3 Investigate: Each of you needs 5 linking cubes.
Assume each face of a linking cube has an area of 1
unit squared.
Number
of Cubes
Surface Area
(square units)
1
2
3
4
5
What patterns do you see in the table?
What happens to the surface area each time you
place another cube on the train?
Explain why the surface area changes in this way.
1.3 Surface Area of Objects Made from Right
Rectangular Prisms
A composite object is an object that is made, or
composed, of other objects.
Examples:
1. Find the surface area of this composite object if
each cube has an edge length of 2 cm.
Method 1: Drawing six views / a net
Method 2: Subtracting overlapping areas
2. Renee wants to cover this object with fabric. How
much fabric will she need to cover the object?
3. The local curling rink shown in the diagram needs
to be painted.
a. Determine the surface area of the structure
b. The roof, windows, and door are not to be
painted. The door is 1 m by 2 m and the window is
4 m by 2 m. Determine the surface area to be
painted.
c. A can of paint covers 300 m2 and costs $45.
Determine the cost of the paint needed.
Assignment: Pages 30-32 #1, 3, 4-12.
Journal: AFQ 10, Reflect
1.4 Surface Area of Other Composite Objects
Examples:
1. Find the surface area of the following composite
object:
2. This cake is covered in frosting. What is the area
of the frosting?
14cm
5cm
5cm
26cm
Assignment: pages 39-43 #1, 3 b d, 4 b, AFQ 7
Study Guide: page 44
Review: pages 45-47 # 2, 3, 4, 5, 8, 13, 15 c, 16 a, 17, 19 b
Practice Test: page 48