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4-5 Squares and Square Roots
Warm Up
Simplify.
1. 52
2. 82
3. 122
4. 152
5. What is a rational number?
Course 3
4-5 Squares and Square Roots
Learn to find square roots.
Course 3
4-5 Squares and Square Roots
Vocabulary
perfect square
Course 3
4-5 Squares and Square Roots
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.
A perfect square has a positive and negative
square root.
Caution!
–49 is not the same as – 49. A negative
number has no real square root.
Course 3
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
–
Course 3
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. 25
–
25 = 5
25 = –5
B. 144
144 = 12
5 is a square root, since 5 • 5 = 25.
–5 is also a square root, since
–5 • –5 = 25.
12 is a square root, since 12 • 12 = 144.
– 144 = –12 –12 is also a square root, since
–12 • –12 = 144.
C. 289
289 = 17
–
Course 3
17 is a square root, since 17 • 17 = 289.
289 = –17 –17 is also a square root, since
–17 • –17 = 289.
4-5 Squares and Square Roots
A square window has an area of 169 square
inches. How wide is the window?
Find the square root of 169 to find the width of
the window. Use the positive square root; a
negative length has no meaning.
132 = 169
So
169 = 13.
The window is 13 inches wide.
Remember!
The area of a square is s2, where s is the
length of a side.
Course 3
4-5 Squares and Square Roots
Check It Out: Example 2
A square shaped kitchen table has an area of
16 square feet. Will it fit through a van door
that has a 5 foot wide opening?
Find the square root of 16 to find the width of
the table. Use the positive square root; a
negative length has no meaning.
16 = 4
So the table is 4 feet wide, which is less than 5
feet, so it will fit through the van door.
Course 3
4-5 Squares and Square Roots
Additional Example 3A: Evaluating Expressions
Involving Square Roots
Evaluate the expression.
3 36 + 7
3 36 + 7 = 3(6) + 7
Course 3
Evaluate the square root.
= 18 + 7
Multiply.
= 25
Add.
4-5 Squares and Square Roots
Additional Example 3B: Evaluating Expressions
Involving Square Roots
Evaluate the expression.
25 + 3
16
4
25 + 3 =
16
4
Course 3
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
Evaluate the expression.
2
25 + 4
2 25 + 4 = 2(5) + 4
Course 3
Evaluate the square root.
= 10 + 4
Multiply.
= 14
Add.
4-5 Squares and Square Roots
Check It Out: Example 3B
Evaluate the expression.
18 + 1
t2
4
18 + 1 = 9 + 1
t2
4
4
Course 3
18 = 9.
t2
=3+ 1
4
Evaluate the square roots.
= 31
4
Add.
4-5 Squares and Square Roots
Try This!
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
Course 3
4-5 Squares and Square Roots
Additional Example 1A: Estimating Square Roots
of Numbers
Each square root is between two
integers. Name the integers. Explain your
answer.
Think: What are
55
72 = 49
82 = 64
perfect squares close
to 55?
49 < 55
64 > 55
55 is between 7 and 8 because 55 is
between 49 and 64.
Course 3
4-5 Squares and Square Roots
Additional Example 1B: Estimating Square Roots
of Numbers Continued
Each square root is between two
integers. Name the integers. Explain
your answer.
Think: What are
– 90
perfect squares close
to 90?
2
–9 = 81
81 < 90
–102 = 100 100 > 90
– 90 is between –9 and –10 because 90 is
between 81 and 100.
Course 3
4-5 Squares and Square Roots
Lesson Quiz
Each square root is between two
integers. Name the two integers.
1.
Course 3
27
5 and 6
2. –
456 –22 and –21
4-5 Squares and Square Roots
Homework:
Workbook pg. 28-29
Course 3