Show that sqrt(3) is an irrational number. (And show and use that if 3 divides n^2, then 3 divides n, and use the fact that every natural number n can be written as n = 3k + a for some natural number k and a = {0, 1, 2}.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 10E
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Show that sqrt(3) is an irrational number. (And show and use that if 3 divides n^2, then 3 divides n, and use the fact that every natural number n can be written as n = 3k + a for some natural number k and a = {0, 1, 2}.) 

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