Using only the definition of rational and irrational numbers, show that if (n + 3)² is irrational, then n is irrational. (In particular, you are not allowed to use any property of irrationals proven in class, or the closure of the rationals.)

Using only the definition of rational and irrational numbers, show that if (n + 3)² is irrational, then n is irrational. (In particular, you are not allowed to use any property of irrationals proven in class, or the closure of the rationals.)

PREALGEBRA

15th Edition

ISBN:9781938168994

Author:OpenStax

Publisher:OpenStax

Chapter7: The Properties Of Real Numbers

Section: Chapter Questions

Problem 408PT: PRACTICE TEST 408. From the numbers -4, 1^, 0, J-, V2, 7, which are (a) integers (b) rational (c)...

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Question

Using only the definition of rational and irrational numbers, show that if (n + 3)² is irrational, then n is
irrational.
(In particular, you are not allowed to use any property of irrationals proven in class, or the closure of the
rationals.)

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