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3. Show that √2+√3 is irrational. Show that √n-1+√n+1 is irrational for every integer n ≥ 1.

3. Show that √2+√3 is irrational. Show that √n-1+√n+1 is irrational for every integer n ≥ 1.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 16E: Prove that if a is rational and b is irrational, then a+b is irrational.
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3. Show that √2 + √3 is irrational. Show that √n-1+√√n + 1 is irrational for every integer n ≥ 1.
Transcribed Image Text:3. Show that √2 + √3 is irrational. Show that √n-1+√√n + 1 is irrational for every integer n ≥ 1.
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