1. FeatureLesson Course 2 Lesson Main LESSON 8-6 Square Roots and Irrational Numbers Problem of the Day 8-6 Calculate the area of the figure below. Include units in your answer

2. FeatureLesson Course 2 Lesson Main LESSON 8-6 Square Roots and Irrational Numbers Problem of the Day 8-6 Area of Rectangle 1 = Base x Height = 4 x 10 = 40 Area of Rectangle 2 = Base x Height = 3 x (8 - 4) = 12 Find 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)r 2 = (1/2)(3.14)1 2 = 1.57 Total Area = 40 + 12 + 1.57 = 53.57 cm 2 or 53.57 square cm cm

3. FeatureLesson Course 2 Lesson Main LESSON 8-6 (For help, go to Lesson 2-1.) Simplify. 2. 8 2 3. 12 2 4. 2 2 5. 7 2 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

4. FeatureLesson Course 2 Lesson Main Solutions 1. Multiply the number by itself. 2.8 2 = 8 8 = 643.12 2 = 12 12 = 144 4.2 2 = 2 2 = 45.7 2 = 7 7 = 49 LESSON 8-6 Square Roots and Irrational Numbers Check Skills You’ll Need 8-6

5. FeatureLesson Course 2 Lesson Main Perfect square: a number that is a square of an integer (Integer: positive whole numbers, their opposites, and zero) 8 2 = 8 8 = 64; so 64 is a perfect square The inverse of squaring a number is finding a square root. 8 2 = 64

6. FeatureLesson Course 2 Lesson Main 81 = 9 81 = 9 2 LESSON 8-6 Simplify 81. Square Roots and Irrational Numbers Quick Check Additional Examples 8-6

7. FeatureLesson Course 2 Lesson Main 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

8. FeatureLesson Course 2 Lesson Main 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.

9. FeatureLesson Course 2 Lesson Main If a positive integer is not a perfect square, its square root is irrational. Rational Irrational

10. FeatureLesson Course 2 Lesson Main 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

11. FeatureLesson Course 2 Lesson Main Estimate each square root. 1. 62. 22 Identify each as rational or irrational. 3.0.6254. 150 LESSON 8-6 about 2 rational about 5 irrational Square Roots and Irrational Numbers Lesson Quiz 8-6

12. FeatureLesson Course 2 Lesson Main Homework: Bring your 3-D object, ruler, scissors Lesson 8-6, pp. 402-403, #s 1-38, all