(a) Prove that if p is a prime number and p|k^2 for some integer k then p|k.(b) Using Part (a), prove or disprove: √3 ∈ Q.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 50E
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(a) Prove that if p is a prime number and p|k^2 for some integer k then p|k.
(b) Using Part (a), prove or disprove: √3 ∈ Q. 

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