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 Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Page 1: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

8-7 Squares and Square Roots

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Page 2: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm UpSimplify.

1. 62

2. 72

3. 112

4. 152

36

49

121

Course 2

8-7 Squares and Square Roots

225

Page 3: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 4: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Learn to find and estimate square roots of numbers.

Course 2

8-7 Squares and Square Roots

Page 5: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Vocabulary

perfect squaresquare rootradical sign

Insert Lesson Title Here

Course 2

8-7 Squares and Square Roots

Page 6: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 7: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 8: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 9: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 10: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 11: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 12: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

√16 = 4 is read as “The square root of 16 is 4.”

Reading Math

Course 2

8-7 Squares and Square Roots

Page 13: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 14: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 15: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 16: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 17: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 18: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 19: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 20: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 21: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 22: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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

Page 23: 8-7 Squares and Square Roots Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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