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Math 3 5 6 7
Lesson 11.1 - Squares and Square Roots
Goal: We will evaluate expressions using square roots.
Vocabulary
TERM
DEFINITION
Square of a number
The number that you get
when you multiply a number
by _______________
Square Root
The number that you multiply
by _____________ to get the
original number
Perfect Squares
Squares of __________
____________
Radical Symbol
The symbol used to show
that you want to take the
__________ _________ of a
number. (The radical symbol
acts as a grouping symbol!!!)
Radicand
The number or expression
under the ____________
_____________
EXAMPLE
Example 1- How do I use my calculator to square
numbers and find square roots?
Task
Square a number
Take the square root of a
number
What I put in my
calculator...
number, x², enter
, number, enter
Example
12² =
4.1² =
-3² =
(-7)² =
√225 =
√40.96 =
√12 =
Example 2- Perfect Squares - MEMORIZE!!!
Use your calculator to find the following square roots:
√1 =
√4 =
√49 =
√64 =
√9 =
√16 =
√81 =
√100 =
√121 =
√25 =
√36 =
√169 =
√196 =
√225 =
√144 =
Example 3- Finding Square Roots
Find the ​two​ square roots of the following numbers:
81
The two square roots of 81 could be ________ or ________ because ________________ = 81
and _________________ = 81.
36
The two square roots of 36 could be ______ or _______ because ________________ = 36
and _______________ = 36.
Guided Practice
Find the ​two​ square roots of the given number:
1.
25
2.
100
3.
144
4.
1
Example 4- Evaluating Square Roots
When evaluating (finding the value of) a square root, we select the answer based on the sign to
the ___________ of the radical symbol.
√25 = 5
(Since there is not a sign on the left of the radical symbol, we assume the answer is
positive)
+ √49 = _______ since the sign on the left is +
- √9 = ______ since the sign on the left is √0 = ______ because ____________ = 0.
√− 64 is ____________________ because _____________ =/ -64 and ____________ =/ -64
Guided Practice
Evaluate the square root:
5.
√81 =
8.
+ √121 =
6.
- √81 =
9.
√− 121 =
7.
- √100 =
Example 5- Solving Equations Involving Square Roots
Solving Equations Review:
To “undo” addition, we ___________________ .
To “undo” subtraction, we ________________ .
To “undo” multiplication, we ______________ .
To “undo” division, we __________________ .
NEW:
To “undo” squaring a number, we _____________________________________________ .
To “undo” taking the square root of a number, we ___________________ .
Solve:
x² = 121
X = ____________________
To solve for x, take the square root of both sides of
The equation. Since we don’t know the sign of “x”,
we write both solutions.
X = _________
A shorter way to write the answer
Solve:
x² = 396
X = ____________________
To solve for x, take the square root of both sides of
The equation. (You may have to round to the
nearest tenth.)
X = _________
A shorter way to write the answer
Solve:
ALWAYS “undo” addition/subtraction first!!
x² + 20 = 101
X = __________
Guided Practice
Solve:
10.
x² = 144
11.
x² = 114
12.
x² + 30 = 130
13.
x² - 25 = 50
Example 6- Application
To solve for x, take the square root of both sides of
The equation.
Pam has enough flooring to cover 196 square feet. If she lays the flooring on a square area,
what is the side length of the largest square she can make?
Area of a square = s²
A = s²
Write an equation for the side length of a square.
________ = s²
Substitute for the area of a square.
√196 =
√s²
Since we are solving for “s” (side length), take the square root of
Both sides of the equation.
S = ______ or ________
But only one makes sense with this problem. Why?
S = ______
Find the side length of the square if A = 39.69 m². (Use the formula A = ​s²)
Guided Practice
12.
Natalie is laying carpeting in her room. She has enough carpeting to cover 2500 square
feet. If her room is a square area, what is the side length of one of the sides of the
square?