4-5 Squares and Square Roots
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
4-5 Squares and Square Roots
Warm Up
Simplify.
1. 52
25
3. 122 144
5. 202 400
2. 82 64
4. 152 225
4-5 Squares and Square Roots
Problem of the Day
A Shakespearean sonnet is a poem
made up of 3 quatrains (4 lines each),
and a couplet (2 lines). Each line is in
iambic pentameter (which means it has
5 iambic feet). So, how many iambic
feet long is a Shakespearean sonnet?
70
4-5 Squares and Square Roots
Sunshine State Standards
MA.8.A.6.2 Make reaonable approximations
of square roots…,and use them to estimate
solutions to problems…
4-5 Squares and Square Roots
Vocabulary
square root: A number that when
multiplied by itself forms a
given product
principal square root: The
nonnegative square root of a
number
perfect square: A number that
has integers as its square roots
4-5 Squares and Square Roots
Think about the relationship between the area of a
square and the length of one of its sides.
area = 36 square units
side length = 6 units because 62= 36
A number that when multiplied by itself to form a
product is the square root of that product. Taking
the square root of a number is the inverse of
squaring the number.
62 = 36
36 = 6
4-5 Squares and Square Roots
Every positive number has two square roots, one
positive and one negative. The radical symbol
indicates the nonnegative or principal square
root. The symbol –
is used to indicate the
negative square root.
The numbers 16, 36, and 49 are examples of
perfect squares. A perfect square is a number
that has integers as its square roots. Other perfect
squares include 1, 4, 9, 25, 64, and 81.
Caution!
–49 is not the same as – 49. A negative
number has no real square root.
4-5 Squares and Square Roots
Additional Example: 1 Finding the Positive and
Negative Square Roots of a Number
Find the two square roots of each number.
A. 49
–
49 = 7
49 = –7
B. 100
100 = 10
– 100 = –10
C. 225
–
7 is a square root, since 7 • 7 = 49.
–7 is also a square root, since
–7 • –7 = 49.
10 is a square root, since 10 • 10 = 100.
–10 is also a square root, since
–10 • –10 = 100.
225 = 15
15 is a square root, since 15 • 15 = 225.
225 = –15
–15 is also a square root,
since –15 • –15 = 225.
4-5 Squares and Square Roots
Check It Out: Example 1
Find the two square roots of each number.
A. 81
81 = 9 • 9 = 81
(–9)(–9) = 81
= ±9
B. 144
144 = 12 • 12 = 144
(–12)(–12) = 144
= ±12
C. 324
324 = 18 • 18 = 324
(–18)(–18) = 324
= ±18
4-5 Squares and Square Roots
Additional Example 2: Application
A square window has an area of 169 square
inches. How wide is the window?
Write and solve an equation to find the area of the
window.
132 = 169
So
169 = 13.
Use the positive square root; a negative length has
no meaning. The window is 13 inches wide.
Remember!
The area of a square is s2, where s is the
length of a side.
4-5 Squares and Square Roots
Check It Out: Example 2
A square window has an area of 225 square
inches. How wide is the window?
152 = 225 so
225
= 15;
The window is 15 inches wide.
4-5 Squares and Square Roots
Additional Example 3A: Evaluating Expressions
Involving Square Roots
Simplify the expression.
3 36 + 7
3 36 + 7 = 3(6) + 7
Evaluate the square root.
= 18 + 7
Multiply.
= 25
Add.
4-5 Squares and Square Roots
Additional Example 3B: Evaluating Expressions
Involving Square Roots
Simplify the expression.
25 + 3
16
4
25 + 3 =
16
4
3
1.5625 +
4
25 = 1.5625.
16
= 1.25 + 3
4
Evaluate the
square roots.
=2
Add.
4-5 Squares and Square Roots
Check It Out: Example 3A
Simplify each expression.
2
121 + 9
2 121 + 9 = 2(11) + 9
= 22 + 9
= 31
4-5 Squares and Square Roots
Check It Out: Example 3B
Simplify each expression.
16 + 2
36
3
16 + 2 = 16 + 2
36
3
3
36
=4 + 2
6
3
= 4 , or 11
3
3
4-5 Squares and Square Roots
Check It Out: Example 3C
Simplify each expression.
–5
336 + 25
–5 336 + 25 = –5 361
= –5(19)
= –95
4-5 Squares and Square Roots
Check It Out: Example 3D
Simplify each expression.
12 • 2
12 • 2
48
48 = 2
48 • 12
= 2 576
= 2(24)
= 48
4-5 Squares and Square Roots
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
4-5 Squares and Square Roots
Lesson Quiz
Find the two square roots of each number.
1. 81 9
2. 2500
50
Evaluate each expression.
3. 3 16 + 1
13
4. 7 9 – 2 49
7
5. Ms. Estefan wants to put a fence around 3 sides
of a square garden that has an area of 225 ft2.
How much fencing does she need?
45 ft
4-5 Squares and Square Roots
Lesson Quiz for Student Response Systems
1. Find two square roots of each number.
64
A. 4
B. 8
C. 9
D. 16
4-5 Squares and Square Roots
Lesson Quiz for Student Response Systems
2. Find two square roots of each number.
6400
A. 4
B. 8
C. 80
D. 800
4-5 Squares and Square Roots
Lesson Quiz for Student Response Systems
3. Evaluate the expression.
A. 44
B. 17
C. 19
D. 72
4-5 Squares and Square Roots
Lesson Quiz for Student Response Systems
4. Evaluate the expression.
A. 4
B. 8
C. 16
D. 40