The Nature of Mathematics, 12th Edition
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Chapter1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
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Section 5.5: Irrational Numbers

5.5 Outline

A.  Pythagorean theorem
      1. perfect squares
      2. square numbers
      3. legs/hypotenuse
B. Square roots
      1. definition
      2. positive square root of n
      3. irrational numbers
      4. the number pi
C. Operations with square roots
      1. simplified square root definition
      2. laws of square roots
          a. square root of zero
          b. square root of a square
          c. multiplication of square roots
          d. division of square roots

5.5 Essential Ideas

One of the most important, and famous, results in mathematics is the Pythagorean theorem: