Name: ____________________
Math 8
Date: _____________
Unit 1 - Perfect squares and cubes
Lesson 1.1 Squares and Square Roots
Pythagoras (about 580–500 B.C.E.) was the leader of a group of academics called the
Pythagoreans. They believed that patterns in whole numbers could help explain the universe.
After this lesson, you will be able to...
 determine the square of a whole number
 determine the square root of a perfect square
Square: If a number is multiplied by itself, the product so
obtained is called the square of that number.
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.
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 ________________.
Prime Factorization
Prime Factors - only has one and itself as its factors. Examples
Prime Factorization - is the prime numbers that multiply to give you the original number
(Bottom row of a factor tree). If each number has a pair, then it is a perfect square:
Use a factor tree to decide if 36 is a perfect square:
Example 1: Identify Perfect Squares
a) Determine the prime factorization of the following numbers: 24, 48, 81.
b) Which of the numbers is a perfect square? Explain.
c) For each number that is a perfect square, draw the square and label its side length.
a)
24
_________________
48
__________________
81
________________
B) To be a perfect square, each prime factor in the prime factorization must occur an even number
of times. ________ and ________ are perfect squares because each prime factor occurs an even
number of times.
 List all the factors of 30 to show it is not a perfect square.
 List all the factors of 64 to show it is a perfect square.
Example 2: Determine the Square of a Number
Determine the area of a square picture with a side length of 17 cm.
Example 3: Determine the Square Root of a Perfect Square
Edgar knows that the square case for his computer has an area of 144 cm2.
What is the side length of the case?
Method 1: Use Inspection
Factorization
Method 2: Use Guess and Check
Example 4: Which number is not a perfect square?
a. 49
b. 64
c. 81
Method 3: Use Prime
d. 86
Example 5:
What is the area of a square with sides of 11 m?
Example 6:
A square has an area of 196 cm2. How long is each side of the square?
Extension: A square picture has area 169 cm2. Find the perimeter of the picture.
Assignment: Pg. 85-86 # 5 – 12, 14, 15, 16, 20 and 21 + Journal #1