8-7 squares and square roots course 2 warm up warm up problem of the day problem of the day lesson...
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8-7 Squares and Square Roots
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpSimplify.
1. 62
2. 72
3. 112
4. 152
36
49
121
Course 2
8-7 Squares and Square Roots
225
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 and Square Roots
Vocabulary
perfect squaresquare rootradical sign
Insert Lesson Title Here
Course 2
8-7 Squares and Square Roots
2
Exponent
Base
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
8-7 Squares and Square Roots
Find each square.
Additional Example 1A: Finding Squares of Numbers
122
Method 1: Use a Model
A = lw
A = 12 · 12
A = 144
The square of 12 is 144.
12
12
Course 2
8-7 Squares and Square Roots
Find each square.
Additional Example 1B: Finding Squares of Numbers
3.52
Method 2: Use a Calculator
Press 3.5 .
3.52 = 12.25
The square of 3.5 is 12.25.
Course 2
88-7Squares and Square Roots
x2 ENTER
Find each square.
Check It Out: Example 1A
102
Method 1: Use a Model
A = lw
A = 10 · 10
A = 100
The square of 10 is 100.
Course 2
8-7 Squares and Square Roots
10
10
Find each square.
Check It Out: Example 1B
5.22
Method 2: Use a Calculator
Press 5.2 .
5.22 = 27.04
The square of 5.2 is 27.04.
Course 2
8-7 Squares and Square Roots
x2 ENTER
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 radicalsign.
Course 2
8-7 Squares and Square Roots
√16 = 4 is read as “The square root of 16 is 4.”
Reading Math
Course 2
8-7 Squares and Square Roots
Find each square root.
The square of 16 is 4.
Course 2
8-7 Squares and Square Roots
√16
Method 1: Use a Model
Additional Example 2A: Finding Square Roots of Perfect Squares
Find each square root.
Press 676 .
The square of 676 is 26.
Course 2
8-7 Squares and Square Roots
x2 ENTER
Additional Example 2B: Finding Square Roots of Perfect Squares
√676Method 2: Use a Calculator
2nd
√676 = 26
Check It Out: Example 2A
The square of 25 is 5.
Course 2
8-7 Squares and Square Roots
Find each square root.
√25
Method 1: Use a Model
Find each square root.
√289Method 2: Use a Calculator
Press 289 .
The square of 289 is 17.
Course 2
8-7 Squares and Square Roots
x2 ENTER
Check It Out: Example 2B
2nd
√289 = 17
Estimate each square root to the nearest whole number. Use a calculator to check your answer.
Additional Example 3A: Estimating Square Roots
36 < 40 < 49
Check
Find the perfect squares nearest 40.
Find the square roots of 36 and 49.
40 is closer in value to 36 than to 49.
6 is a reasonable estimate.
√36 < √40 < 49√
6 < 40 < 7√
40 6√
40 6.32455532033√ Use a calculator to approximate √40.
√40
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.
64 < 79 < 81
Check
Find the perfect squares nearest 79.
Find the square roots of 64 and 81.
79 is closer in value to 81 than to 64.
√79
79 9√
79 8.8881944√
8 < 79 < 9√
√64 < √79 < 81√
Use a calculator to approximate √79.
9 is a reasonable estimate.Course 2
8-7 Squares and Square Roots
Check It Out: Example 3A
Insert Lesson Title Here
Estimate each square root to the nearest whole number. Use a calculator to check your answer.
√22
16 < 22 < 25
Check
Find the perfect squares nearest 22.
Find the square roots of 16 and 25.
22 is closer in value to 25 than to 16.
4 < 22 < 5√
22 5√
22 4.690415759√
√16 < √22 < 25√
Use a calculator to approximate√22.
5 is a reasonable estimate.Course 2
8-7 Squares and Square Roots
Check It Out: Example 3B
Insert Lesson Title Here
√53
49 < 53 < 64
Check
Find the perfect squares nearest 53.
Find the square roots of 49 and 64.
53 is closer in value to 49 than to 64.
7 < 53 < 8√
53 7√
53 7.2801098828√
√49 < √53 < 64√
Use a calculator to approximate√53.
Estimate each square root to the nearest whole number. Use a calculator to check your answer.
7 is a reasonable estimate.Course 2
8-7 Squares and Square Roots
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.
Additional Example 4: Recreation Application
121 < 125 < 144 Find the perfect squares nearest 125.
Find the square roots of 121 and 144.
Each side of the search area is about 11 miles long.
125 is closer to 121 than to 144.
The length of each side of the square is √125 .
< < √125√121 √144
11 < < 12√125
√125 11
Course 2
8-7 Squares and Square Roots
Check It Out: Example 4A 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.
Insert Lesson Title Here
The length of each side of the square is √168 .
144 < 168 < 169 Find the perfect squares nearest 168.
Find the square roots of 144 and 169.
< < √168√144 √169
12 < < 13√168
√168 13
Each side of the tent is about 13 feet long.
168 is closer to 169 than to 144.
Course 2
8-7 Squares and Square Roots
Lesson Quiz
Find each square.
1. 162
2. (3.5)2
Estimate each square root to the nearest whole number. Use a calculator to check.
3.
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?
12.25
256
Insert Lesson Title Here
4 7√15 4. √52
4.5 ft
Course 2
8-7 Squares and Square Roots