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1-3 Real Numbers and the Number Line

1-3 Real Numbers and the Number Line. The radical symbol indicates a nonnegative square root. Problem 1: Simplifying Square Root Expressions. What is the simplified form of each expression. Problem 1: Simplifying Square Root Expressions.

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1-3 Real Numbers and the Number Line

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  1. 1-3 Real Numbers and the Number Line

  2. The radical symbol indicates a nonnegative square root

  3. Problem 1: Simplifying Square Root Expressions What is the simplified form of each expression

  4. Problem 1: Simplifying Square Root Expressions What is the simplified form of each expression

  5. Problem 1: Simplifying Square Root Expressions What is the simplified form of each expression

  6. Problem 1: Simplifying Square Root Expressions What is the simplified form of each expression

  7. The square of an integer is called a perfect square. 49 is a perfect square because is a perfect square. When a radicand is not a perfect square, you can estimate the square root.

  8. Problem 2: Estimating a Square Root Lobster eyes are made of tiny square regions. Under a microscope, the surface of the eye looks like graph paper. A scientist measures the area of one of the squares to be 386 square microns. What is the approximate side of the square to the nearest micron?

  9. Problem 2: Estimating a Square Root What is the value of to the nearest integer

  10. Problem 4: Comparing Real Numbers Inequality: a mathematical sentence that compares the values of two expressions using an inequality symbol. < LESS THAN > GREATER THAN  LESS THAN OR EQUAL TO  GREATER THAN OR EQUAL TO

  11. What is an inequality that compares What is an inequality that compares

  12. Problem 5: Graphing and Ordering Real Numbers What is the order of from least to greatest. Then order on a number line.

  13. Problem 5: Graphing and Ordering Real Numbers What is the order of from least to greatest. Then order on a number line.

  14. Problem 3: Classifying Real Number

  15. Rational Number: In the form , where a and b are integers and In decimal form they are terminating decimal such as 5.45 or a repeating decimal such as 0.416666… which you can write as

  16. Natural numbers: also called counting numbers and are the ones you count with {1, 2, 3, …} Whole Numbers: include the natural numbers, but also includes zero {0, 1, 2, 3, …} Integers: The whole numbers, plus their respective negative numbers {…, -3, -2, -1, 0, 1, 2, 3, …}

  17. Irrational numbers: cannot be written as a fraction. In decimal form, irrational numbers do not terminate or repeat. (some square roots are rational and some are irrational) (if a whole number is not a perfect square, its square is irrational ex:)

  18. Rational numbers and irrational numbers form the set of Real numbers

  19. To which subsets of the real number system does each number belong? • 15

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