Download 3.1 Squares and Square Roots key

Name: ___________________
Math 8 Numeracy
Date: ______________
3.1A - Squares and Square Roots
Square:
If a number is multiplied by itself, the product so obtained is called the square of that number.
The square root of a number:
is the number that, when squared (multiplied by itself), is equal to the given number. For example, the
square root of 16 is ________________
In this section we will be looking at the relationship between the area of a square and
its side length.
Square
Side Length
Area
So the area of the square is found using the
formula:
A = S x S or
A =S2
If we can represent an area using squares then it is a perfect square or square number.
For example,
The numbers 1, 4 and 9 are all perfect squares.
Finish the table on the right. You will need to remember these prefect squares:
Do you think that 20 is a perfect square? Explain:
There are 4 ways to determine if a number is a perfect square:
1.
2.
3.
4.
Try to draw the square
Write a division sentence to show that the quotient is equal to the divisor
Find the factors of the number
Prime factorization
We will now look at how to use each of these criteria:
1) Try to Draw the Square
Is 36 a perfect square?
Is 20 a perfect square?
1. List the factors of each number.
a) 8
1×
=8
b) 16
1×
=
2×
=8
2×
=
Factors of 8:
×
=
Factors of 16:
c) 20
d) 32
Factors of 20:
Factors of 32:
2. Calculate.
a) 52
=5×5
b) 22 =
=
=
c) 82 =
d) 122=
=
=
×
3. Solve using mental math.
a) 25 = 5 ×
c) 64 =
×8
b) 4 = 2 ×
d) 100 =
× 10
Identify Perfect Squares
a) What is the prime factorization of 24 and 81?
Solution
Prime Factorization
● A number written as the product of its prime factors
● Example: 2 × 2 × 3 = 12
Use a factor tree.
The prime factorization of 24 is
×
×2×
.
The prime factorization of 81 is
×
×3×
.
b) Is 24 or 81 a perfect square?
Perfect square
●
A number that is the square of a whole number
●
Examples: 12 = 1 × 1 = 1
32 = 3 × 3 = 9
So, 1, 4, 9, 16, … are perfect squares.
22 = 2 × 2 = 4
42 = 4 × 4 = 16
To be a perfect square, there must be pairs of each prime factor in the factor tree.
81 = 3 × 3 × 3 × 3
There are four factors of
. So, 81 is a perfect square.
24 =
×
×
×
There are three factors of 2, and
factor of 3.
24 is not a perfect square, because the factors 2 and 3 each appear an
number of times.
(even or odd)
Example: Draw a factor tree for each number.
a) 45
b) 100
Textbook Page #85 Questions # 5-12
2 pairs of 3