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1-3 Real Numbers and the Number Line
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The radical symbol indicates a nonnegative square root
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Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression 81
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Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression 9 16
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Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression 64
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Problem 1: Simplifying Square Root Expressions
What is the simplified form of each expression 1 36
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The square of an integer is called a perfect square
The square of an integer is called a perfect square. 49 is a perfect square because 7 2 =49 is a perfect square. When a radicand is not a perfect square, you can estimate the square root.
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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?
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Problem 2: Estimating a Square Root
What is the value of to the nearest integer
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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
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What is an inequality that compares 17 𝑎𝑛𝑑 4 1 3 What is an inequality that compares 129 𝑎𝑛𝑑 11.52
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Problem 5: Graphing and Ordering Real Numbers
What is the order of 4 , 0.4, − 2 3 , 2 , 𝑎𝑛𝑑 −1.5 from least to greatest. Then order on a number line.
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Problem 5: Graphing and Ordering Real Numbers
What is the order of 3.5, −2.1, 9 , − 7 2 , 𝑎𝑛𝑑 5 from least to greatest. Then order on a number line.
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Problem 3: Classifying Real Number
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Rational Number: In the form 𝑎 𝑏 , where a and b are integers and 𝑏≠0
Rational Number: In the form 𝑎 𝑏 , where a and b are integers and 𝑏≠0. In decimal form they are terminating decimal such as 5.45 or a repeating decimal such as … which you can write as
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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, …}
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Irrational numbers: cannot be written as a fraction
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: 3 = …)
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Rational numbers and irrational numbers form the set of Real numbers
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To which subsets of the real number system does each number belong?
15 −1.4583 57 3 10
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