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

Algebra 1 Notes: Lesson 2-7: Square Roots and Real Numbers. Objectives. Distinguish between Rational and Irrational Numbers Graph sets of Real Numbers on the n umber line Organize Real Numbers into numerical order. Vocabulary Square Root One of two equal factors of a number

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

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  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 Numbers Irrational 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

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

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

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

  18. Example 2 • Name the set or sets of numbers to which each real number belongs. • a) = 4.1231056… Irrational number • Rational number • = 13 Rational, integer, whole, natural • -327 Rational 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. • 14

  24. Example 4 • Replace each _____ with <, >, or = to make each sentence true. • 14 = 14

  25. Example 4 • Replace each _____ with <, >, or = to make each sentence true. • 14 = = 14

  26. Example 4 • Replace each _____ with <, >, or = to make each sentence true. • 14 = = 14 • = 6.9282032…

  27. Example 4 • Replace each _____ with <, >, or = to make each sentence true. • 14 = = 14 • = 6.9282032… • = 6.9999999…

  28. Example 4 • Replace each _____ with <, >, or = to make each sentence true. • 14 = = 14 • < • = 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)

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