6. (i) Sketch the proof of the existence of a positive number satisfying the equation a2 = 5. We denote this positive number by the symbol V5. (ii) Prove that the number V5 is not a rational number (that is, it cannot be expressed as a quotient of integers).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 78E
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6. (i) Sketch the proof of the existence of a positive number satisfying the
equation x2 = 5. We denote this positive number by the symbol V5.
(ii) Prove that the number V5 is not a rational number (that is, it cannot
be expressed as a quotient of integers).
Transcribed Image Text:6. (i) Sketch the proof of the existence of a positive number satisfying the equation x2 = 5. We denote this positive number by the symbol V5. (ii) Prove that the number V5 is not a rational number (that is, it cannot be expressed as a quotient of integers).
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