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# Assuming the truth of the theorem that stales that is ISBN: 9780073383095 37

## Solution for problem 46E Chapter 1.SE

Discrete Mathematics and Its Applications | 7th Edition

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Problem 46E

Assuming the truth of the theorem that stales that is irrational whenever n is a positive integer that is not a perfect square, prove that is irrational.

Step-by-Step Solution:

Solution:Step 1In this problem we have to prove that is irrational assuming the truth of the theorem that states that is irrational whenever n is positive integer and is not a perfect square.We will prove this problem by method of contradiction.Any number which can be written in the form of where are integer and .Step 2Let us assume that is rational.We have where p and q are integer and q is not equal to 0.On squaring both side of equation we get Or, +3=. [using formula Or, On subtracting 5 on both side of equation we get On dividing both side by 2 we get

Step 3 of 3

##### ISBN: 9780073383095

Since the solution to 46E from 1.SE chapter was answered, more than 248 students have viewed the full step-by-step answer. The answer to “Assuming the truth of the theorem that stales that is irrational whenever n is a positive integer that is not a perfect square, prove that is irrational.” is broken down into a number of easy to follow steps, and 27 words. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 46E from chapter: 1.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. This full solution covers the following key subjects: irrational, prove, assuming, perfect, Positive. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.

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