1. Perfect Squares, Square Roots, and the Order of Operations
So, what makes a number a perfect square?
A perfect square is a number that is the product of any integer multiplied to itself.
For example, 1 x 1 = 1 and 2 x 2 = 4…
1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are all of the perfect squares found from 1 – 100.

2. Another reason perfect squares are considered “perfect” can be justified with the visual shown below.
On the provided piece of graph paper, draw your own perfect square example. Remember each side of the square should be the same length. The squares in the center is your perfect square number.

3. The square root of a number is the opposite (or reverse) of finding the perfect square. It is uncovering the base number that was multiplied to itself. We can identify a square root problem with this symbol:
This symbol can also be referred to as a “radical.”

4. “The square root of 9 equals 3.”
Create your own square root problems. Place a perfect square inside the radical and solve it.
= ____

5. Sometimes, exponents and square root symbols find their way into numerical expressions.
It is our job to comprehend the situation and, most likely, evaluate the expression. 2
x (2 + 8)

6. x (2 + 8) 2
To solve this problem, we have to follow the ORDER OF OPERATIONS. By solving it in a specific order and with accurate calculations, we are guaranteed to evaluate it correctly.
Scared?

7. [(P)] E M/D A/S PEMDAS Time!
Remember “Please Excuse My Dear Aunt Sally?”
[(P)] E
M/D
A/S
Parentheses (and brackets) are first to solve.
Exponents and Radicals are next to complete.
Multiplication or Division
Addition or Subtraction finalizes the process.
Your final answer should be one simplified expression or number.

8. x (2 + 8) 2
Hint! Break up the expressions into smaller, more manageable parts. Look for the addition and subtraction operations (not including the one in the parentheses). These will help separate the expression.

9. x (2 + 8) 2 x
266 – 15
251

10. x 2

11. 3
72 – 2 x