Transcript square root

8-7 Squares and Square Roots
Warm Up
Problem of the Day
Lesson Presentation
Course 2
8-7 Squares and Square Roots
Warm Up
Simplify.
1. 62
36
2. 72
49
3. 112
121
4. 152
225
Course 2
8-7 Squares and Square Roots
Problem of the Day
The square of two whole numbers are
16 units apart on a number line. What
are the two numbers?
3 and 5
Course 2
8-7 Squares and Square Roots
Learn to find and estimate square roots of
numbers.
Course 2
8-7 Squares
Insert Lesson
Title Here
and Square
Roots
Vocabulary
perfect square
square root
radical sign
Course 2
8-7 Squares and Square Roots
A square with sides that
measure 3 units each has
an area of 3 · 3, or 32.
Notice that the area of
the square is represented
by a power in which the
base is the side length
and the exponent is 2. A
power in which the
exponent is 2 is called a
square.
Course 2
Exponent
2
Base
8-7 Squares and Square Roots
Additional Example 1A: Finding Squares of Numbers
Find each square.
122
Method 1: Use a Model
12
A = lw
12
A = 12 · 12
A = 144
The square of 12 is 144.
Course 2
88-7 Squares and Square Roots
Additional Example 1B: Finding Squares of Numbers
Find each square.
3.52
Method 2: Use a Calculator
Press 3.5
x2
ENTER
.
3.52 = 12.25
The square of 3.5 is 12.25.
Course 2
8-7 Squares and Square Roots
Check It Out: Example 1A
Find each square.
102
Method 1: Use a Model
10
A = lw
10
A = 10 · 10
A = 100
The square of 10 is 100.
Course 2
8-7 Squares and Square Roots
Check It Out: Example 1B
Find each square.
5.22
Method 2: Use a Calculator
Press 5.2
x2
ENTER
.
5.22 = 27.04
The square of 5.2 is 27.04.
Course 2
8-7 Squares and Square Roots
A perfect square is the square of a whole
number. The number 49 is a perfect square
because 49 =72 and 7 is a whole number. The
number 6.25 is not a perfect square.
The square root of a number is one of
the two equal factors of the number.
Four is a square root of 16 because
4 · 4 = 16. The symbol for a square
root is √
, which is called a radical
sign.
Course 2
8-7 Squares and Square Roots
Reading Math
√16 = 4 is read as “The square root of 16
is 4.”
Course 2
8-7 Squares and Square Roots
Additional Example 2A: Finding Square Roots of
Perfect Squares
Find each square root.
√16
Method 1: Use a Model
The square of 16 is 4.
Course 2
8-7 Squares and Square Roots
Additional Example 2B: Finding Square Roots of
Perfect Squares
Find each square root.
√676
Method 2: Use a Calculator
Press
2nd
x2 676
ENTER
√676 = 26
The square of 676 is 26.
Course 2
.
8-7 Squares and Square Roots
Check It Out: Example 2A
Find each square root.
√25
Method 1: Use a Model
The square of 25 is 5.
Course 2
8-7 Squares and Square Roots
Check It Out: Example 2B
Find each square root.
√289
Method 2: Use a Calculator
Press
2nd
x2 289
ENTER
√289 = 17
The square of 289 is 17.
Course 2
.
8-7 Squares and Square Roots
Additional Example 3A: Estimating Square Roots
Estimate each square root to the nearest whole
number. Use a calculator to check your answer.
√40
36 < 40 < 49 Find the perfect squares nearest 40.
√36 < √40 <√49
6 <√40 < 7
√ 40  6
Find the square roots of 36 and 49.
40 is closer in value to 36 than to 49.
Check
√40  6.32455532033 Use a calculator to approximate √40.
6 is a reasonable estimate.
Course 2
8-7 Squares and Square Roots
Additional Example 3B: Estimating Square Roots
Estimate each square root to the nearest whole
number. Use a calculator to check your answer.
√79
64 < 79 < 81
Find the perfect squares nearest 79.
√64 < √79 <√81
8 <√79 < 9
√ 79  9
Find the square roots of 64 and 81.
79 is closer in value to 81 than to 64.
Check
√79  8.8881944 Use a calculator to approximate √79.
9 is a reasonable estimate.
Course 2
8-7 Insert
Lesson
Title Here
Squares
and Square
Roots
Check It Out: Example 3A
Estimate each square root to the nearest whole
number. Use a calculator to check your answer.
√22
16 < 22 < 25
Find the perfect squares nearest 22.
√16 < √22 <√25
4 <√22 < 5
√22  5
Find the square roots of 16 and 25.
22 is closer in value to 25 than to 16.
Check
√22  4.690415759
Use a calculator to approximate√22.
5 is a reasonable estimate.
Course 2
8-7 Insert
Lesson
Title Here
Squares
and Square
Roots
Check It Out: Example 3B
Estimate each square root to the nearest whole
number. Use a calculator to check your answer.
√53
49 < 53 < 64
Find the perfect squares nearest 53.
√49 < √53 <√64
7 <√53 < 8
√53  7
Find the square roots of 49 and 64.
53 is closer in value to 49 than to 64.
Check
√53  7.2801098828
Course 2
Use a calculator to
approximate √53.
7 is a reasonable estimate.
8-7 Squares and Square Roots
Additional Example 4: Recreation Application
A Coast Guard boat searching for a lost sailboat
covers a square area of 125 mi2. What is the
approximate length of each side of the square
area? Round your answer to the nearest mile.
The length of each side of the square is √125 .
121 < 125 < 144
Find the perfect squares nearest 125.
√121 < √125 < √144
11
< √125 < 12
√125  11
Find the square roots of 121 and 144.
125 is closer to 121 than to 144.
Each side of the search area is about 11 miles long.
Course 2
8-7 Insert
Lesson
Title Here
Squares
and Square
Roots
Check It Out: Example 4
A tent was advertised in the newspaper as having
an enclosed square area of 168 ft2. What is the
approximate length of the sides of the square
area? Round your answer to the nearest foot.
The length of each side of the square is √168
.
144 < 168 < 169
Find the perfect squares nearest 168.
√144 < √168 < √169
12 < √16 < 13
8
√168  13
Find the square roots of 144 and 169.
168 is closer to 169 than to 144.
Each side of the tent is about 13 feet long.
Course 2
8-7 Squares
Insert Lesson
and Square
Title Here
Roots
Lesson Quiz
Find each square.
1. 162
256
2. (3.5)2 12.25
Estimate each square root to the nearest
whole number. Use a calculator to check.
3. √15
4
4. √52
7
5. A square dining room table has an area of 20 ft2.
What is the length of each side of the table, to
the nearest tenth? 4.5 ft
Course 2