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LESSON 8-6Square Roots and Irrational Numbers

Problem of the Day

8-6

Calculate the area of the figure below. Include units in your answer

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LESSON 8-6Square Roots and Irrational Numbers

Problem of the Day

8-6

Area of Rectangle 1 = Base x Height = 4 x 10 = 40Area of Rectangle 2 = Base x Height = 3 x (8 - 4) = 12Find the area of the circle. Because it's a half-circle, we multiply the area by (1/2).Area of Circle = (1/2)(3.14)r2 = (1/2)(3.14)12 = 1.57Total Area = 40 + 12 + 1.57 = 53.57 cm2 or 53.57 square cm

cm

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LESSON 8-6

(For help, go to Lesson 2-1.)

Simplify.

2. 82 3. 122

4. 22 5. 72

Square Roots and Irrational Numbers

Check Skills You’ll Need

1. Vocabulary Review How do you find the square of a number?

Check Skills You’ll Need

8-6

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Solutions 1. Multiply the number by itself.

2. 82 = 8 • 8 = 64 3. 122 = 12 • 12 = 144

4. 22 = 2 • 2 = 4 5. 72 = 7 • 7 = 49

LESSON 8-6Square Roots and Irrational Numbers

Check Skills You’ll Need

8-6

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Perfect square: a number that is a square of an integer(Integer: positive whole numbers, their opposites, and zero)

82 = 8 • 8 = 64; so 64 is a perfect square

The inverse of squaring a number is finding a square root. 82 = 64

8

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81 = 9 81 = 92

LESSON 8-6

Simplify 81.

Square Roots and Irrational Numbers

Quick Check

Additional Examples

8-6

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60 is between 7 and 8.

Estimate the value of 60.

LESSON 8-6

Find perfect squares close to 60.49 < 60 < 64

Simplify.7 < 60 < 8

60 8.Since 60 is closer to 64 than it is to 49,

Square Roots and Irrational Numbers

Quick Check

Additional Examples

8-6

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Rational number: a number that can be written as a fraction (ratio of two integers)

Irrational number: a number that cannot be written as a fraction. If it’s written as a decimal, it does not terminate nor does it repeat.

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If a positive integer is not a perfect square, its square root is irrational.

Rational

Irrational

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c. –0.5167

b. 30

Identify each number as rational or irrational.

a. 121 rational 121 is a perfect square.

LESSON 8-6

irrational 30 is not a perfect square.

rational It is a terminating decimal.

d. 29.2992999. . . irrational The decimal neither terminates nor repeats.

Square Roots and Irrational Numbers

Quick Check

Additional Examples

8-6

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Estimate each square root.

1. 6 2. 22

Identify each as rational or irrational.

3. 0.625 4. 150

LESSON 8-6

about 2

rational

about 5

irrational

Square Roots and Irrational Numbers

Lesson Quiz

8-6

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Homework:Bring your 3-D object, ruler, scissorsLesson 8-6, pp. 402-403, #s 1-38, all