1. Algebra 1 Notes: Lesson 2-7: Square Roots and Real Numbers

2. Objectives Distinguish between Rational and Irrational Numbers Graph sets of Real Numbers on the number line Organize Real Numbers into numerical order

3. Vocabulary Square Root One of two equal factors of a number Perfect Square Radical Sign

4. Vocabulary Square Root One of two equal factors of a number Perfect Square Solution of any number squared Radical Sign

5. Vocabulary Square Root Perfect Square Radical Sign If it comes in the problem, it only wants the positive solution.

6. Indicates the principal square root of 64 Indicates the negative square root of 64 Indicates both square roots of 64

7. Example 1 Find each square root. a) b)

8. Example 1 Find each square root. a) b) = 0.12

9. Vocabulary Irrational Numbers examples…. Real Numbers

10. Vocabulary Irrational Numbers examples…. Real Numbers - Any number on the number line. - Every number you know about.

11. Real Numbers Rational NumbersIrrational Numbers Integers Whole Numbers Natural Numbers

12. Example 2 Name the set or sets of numbers to which each real number belongs. a)

13. Example 2 Name the set or sets of numbers to which each real number belongs. a) = 4.1231056…

14. Example 2 Name the set or sets of numbers to which each real number belongs. a) = 4.1231056… Irrational number b)

15. Example 2 Name the set or sets of numbers to which each real number belongs. a) = 4.1231056… Irrational number b) Rational number c)

16. Example 2 Name the set or sets of numbers to which each real number belongs. a) = 4.1231056… Irrational number b) Rational number c) = 13

17. Example 2 Name the set or sets of numbers to which each real number belongs. a) = 4.1231056… Irrational number b) Rational number c) = 13 Rational, integer, whole, natural d) -327

18. Example 2 Name the set or sets of numbers to which each real number belongs. a) = 4.1231056… Irrational number b) Rational number c) = 13 Rational, integer, whole, natural d) -327Rational number and integer

19. Example 3 Graph each solution set. a) x > -2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

20. Example 3 Graph each solution set. a) x > -2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

21. Example 3 Graph each solution set. a) x > -2 b) a ≤ 4.5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

22. Example 3 Graph each solution set. a) x > -2 b) a ≤ 4.5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

23. Example 4 Replace each _____ with, or = to make each sentence true. a) 14

24. Example 4 Replace each _____ with, or = to make each sentence true. a) 14 = 14

25. Example 4 Replace each _____ with, or = to make each sentence true. a) 14 = = 14 b)

26. Example 4 Replace each _____ with, or = to make each sentence true. a) 14 = = 14 b) = 6.9282032…

27. Example 4 Replace each _____ with, or = to make each sentence true. a) 14 = = 14 b) = 6.9282032… = 6.9999999…

28. Example 4 Replace each _____ with, or = to make each sentence true. a) 14 = = 14 b) < = 6.9282032… = 6.9999999…

29. Example 5 Write in order from least to greatest. = 2.63636363… = -2.64575131… = 2.66666666… = -2.65,,,

30. Homework Pgs. 107: 20 – 56 (evens)