LESSON 11.1 Using Squares and Square Roots
Goal: Evaluate expressions involving square roots.
Vocabulary
Square of a number: The answer when you multiply a number by _____________________.
Example:
Square root: The number that you multiply by _________________ to get the answer you want.
Example:
Perfect squares: Numbers whose square root is an ____________________________.
Example:
Radical symbol: The symbol used to show that you want to take the __________________________, cube
root, etc. of a number. Acts as a grouping symbol!
Example:
Radicand: The number or expression under the ___________________________________.
Example:
Example 1 – How to square numbers and find square roots with your calculator.
USING YOUR CALCULATOR do the following examples:
What you are trying to do....
What you put into the calculator:
You try it!
Square a number
number, x², enter
16² =
4.3² =
-6² =
(-6)² =
Raise a number to ANY power
number,
, power, enter
18² =
9³ =
Take the square root of a number
2nd , x², number, ), enter
1225  40.96 
(Multiview:
Take ANY root of a number
root, 2nd ,
10 
, number, enter)
, number, enter
3
125 =
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Example 2 – PERFECT SQUARES – MEMORIZE THEM!!!
Using your calculator find the following square roots:
√1 =
√49 =
√169 =
√64 =
√196 =
√4 =
√81 =
√225 =
√9 =
√100 =
√16 =
√121 =
√25 =
√144 =
√36 =
Why do you think these are called perfect squares? Which is the “root” ? Which is the perfect square?
EXAMPLE 3 - Finding Square Roots
Find the two square roots of the numbers 64 and 100.
a.
The square roots of 64 could be _____or______ because __________ = 64
and __________ = 64.
b. The square roots of 100 could be _____ or _____ because __________ = 100
and __________ = 100.
Guided Practice
Find the two possible square roots of the number.
1) 16
2) 81
3) 121
4) 1
EXAMPLE 4 - Evaluating Square Roots OF NUMBERS
When evaluating (finding the value of) a square root, we select the
answer based on the sign on the _____________________________
of the radical symbol.
a.
You know that
25 = _____ since there is not sign on the
outside of the radical symbol,
we assume the answer is positive.
b. You know that + 4 = ____ since the sign is +.
c. You know that – 4 = _____ since the sign is -.
The expression
25
is read “the positive
square root of 25”
or simply “the
square root of 25”
d.
0 = _____ because __________ = 0.
e.
 25 is _____________________________ because ___________ ≠ -25 and ___________ ≠ -25
Guided Practice
Evaluate the square root.
5)
6) –
9
9
144
9)
-144
Page
8) +
2
7) – 25
EXAMPLE 5 - Solving a Square Root Equation
Review of solving equations:
When we wanted to “undo” adding a number we ______________________.
When we wanted to “undo” subracting a number we ______________________.
When we wanted to “undo” multiplying by a number we _____________________.
NEW:
When we wanted to “undo” dividing by a number we ______________________.
To “undo” squaring a number we __________________________________________.
To “undo” taking the square root of a number we ________________________________________.
a. Solve: x 2  225
x² =
225
To solve for x, take the square root of both sides of the equation
x = ______________
Since we don’t know the sign of “x”, we write both solutions.
x = _______
A shorter way to write the answer
b. Solve: x 2 = 187
x² =
187
To solve for x, take the square root of both sides of the equation
x = ______________
c. Solve: x 2 + 20 = 101
x² =
Square roots are not always integers! Round to the nearest tenth.
ALWAYS “undo” adding first!
___
To solve for x, take the square root of both sides of the equation
x = ______________
Guided Practice
SOLVE:
10) x = 49
2
11) x = 110
2
12) x + 25 = 100
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Example 6 - Applications
a. 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 = bh OR s² since b and h are the same. We will use…..
A = s²
A = s²
Write equation for side length of a square.
________ = s²
Substitute in the area of the square
196  s2
s = _______ or ________
s = _______
Since we are solving for “s” (the side length), take the square root of both
sides of the equation.
Positive and negative version of solution
Only one makes sense. WHY????
b. Find the side length of the square if A = 39.69 m2. Use the formula A = s².
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Guided Practice
12. Pam has enough flooring to cover 2500 square feet. If she lays the flooring on a square area, what is
the side length of one of the sides of the square?