N-RN.3

Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Internet Resources (Videos, Websites, etc.)

Google PDF

  1. Why is the sum of a rational and irrational number irrational? (PROOF)

MathForum.org

  1. Why is the product of a nonzero rational number and an irrational number irrational?

Mathematics Assessment Project (MAP)

  1. N01: The Real Number System

Shmoop

  1. Explanation
  2. Quiz

Wiki.Answers.com

  1. Why is the sum of two rational numbers rational?

Why is the product of rational numbers rational? (Explanation)

Any rational number can be written as one integer divided by another, 
right?  That's the definition of a rational number. Now, suppose you 
have two of them, and you multiply them together. What happens? 

  a   c   a * c
  - * - = -----
  b   d   b * d

Now, if a and c are integers, then a*c is also an integer, right?  
Similarly for b and d. So the product of two rational numbers must be 
a rational number.

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