Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Question
Chapter 6.6, Problem 40WE
To determine
To Prove:
If x is rational number and z is irrational number , prove that x+z is irrational number.
Expert Solution & Answer
Explanation of Solution
Concept Used:
Sum of two rational numbers is a rational number.
Calculation:
Given :
x is rational number and z is irrational number.
To prove :
x+z is irrational .
Proof:
On the contrary, assume that x+z is a rational number.
Since x is rational number , -x is also rational number.
Now, x+z and −x are rational numbers and we know that rational numbers are closed under addition.
So, (x+z) + (-x) is a rational number.
Hence, z is a rational number , which contradicts the given information that z is an irrational number.
So, our assumption that x+z is a rational number was wrong.
Hence, x+z is an irrational number.
Hence proved.
Chapter 6 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
Ch. 6.1 - Prob. 1OECh. 6.1 - Prob. 2OECh. 6.1 - Prob. 3OECh. 6.1 - Prob. 4OECh. 6.1 - Prob. 5OECh. 6.1 - Prob. 6OECh. 6.1 - Prob. 7OECh. 6.1 - Prob. 8OECh. 6.1 - Prob. 9OECh. 6.1 - Prob. 10OE
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Prob. 12MPS
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