Using the special axiom of fields for irrational numbers and complex numbers. Prove a and b a.)if 0 ≠ p ∈ Q and x ∉ Q, then r+x ∉ Q and rx ∉ Q.  b.) sqrt(11) is irrational

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 53E
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Using the special axiom of fields for irrational numbers and complex numbers.

Prove a and b
a.)if 0 ≠ p ∈ Q and x ∉ Q, then r+x ∉ Q and rx ∉ Q. 
b.) sqrt(11) is irrational

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