Answered: (b) Prove that √2+√3 is irrational.…

(b) Prove that √2+√3 is irrational. Hint: Assume that √2+√3 is rational. Construct, under this assumption, another rational number that involves only one square root.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 13E: 13. Prove that if and are rational numbers such that then there exists a rational number such...

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Question

(b) Prove that √√2 + √√3 is irrational.
Hint: Assume that √2+√3 is rational. Construct, under this assumption, another rational
number that involves only one square root.

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