Modeling Squares and Finding the Square Root of a Number
Learning Outcomes
- Find the square root of of perfect square
- Explain why the square root of a negative number is not a real number
Simplify Expressions with Square Roots
To start this section, we need to review some important vocabulary and notation. Remember that when a number is multiplied by itself, we can write this as , which we read aloud as "n squared". For example, is read as "8 squared". We call the square of because . Similarly, is the square of , because .Square of a Number
If , then is the square of .

Perfect Squares
A perfect square is the square of a whole number.
Square Roots
Sometimes we will need to look at the relationship between numbers and their squares in reverse. Because , we say is the square of . We can also say that is a square root of .Square Root of a Number
A number whose square is is called a square root of . If , then is a square root of .Square Root Notation
.

example
Simplify: ⓐ ⓑ .Answer: Solution
try it
[ohm_question]146618[/ohm_question]example
Simplify. ⓐ ⓑAnswer: Solution
ⓐ | |
The negative is in front of the radical sign. |
ⓑ | |
The negative is in front of the radical sign. |
try it
[ohm_question]146619[/ohm_question]Square Root of a Negative Number
Can we simplify Is there a number whose square is None of the numbers that we have dealt with so far have a square that is . Why? Any positive number squared is positive, and any negative number squared is also positive. In the next chapter we will see that all the numbers we work with are called the real numbers. So we say there is no real number equal to . If we are asked to find the square root of any negative number, we say that the solution is not a real number.example
Simplify: ⓐ ⓑ .Answer: Solution ⓐ There is no real number whose square is . Therefore, is not a real number. ⓑ The negative is in front of the radical sign, so we find the opposite of the square root of .
The negative is in front of the radical. |