A calculator display shows that = 1.414213562, and This

Chapter 4, Problem 1E

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QUESTION:

A calculator display shows that \(\sqrt{2}\) = 1.414213562, and \(1.414213562=\frac{1414213562}{1000000000}\). This suggests that \(\sqrt{2}\) is a rational number, which contradicts Theorem 4.7.1. Explain the discrepancy.

Text Transcription:

sqrt 2

1.414213562 = 1414213562/1000000000

Questions & Answers

QUESTION:

A calculator display shows that \(\sqrt{2}\) = 1.414213562, and \(1.414213562=\frac{1414213562}{1000000000}\). This suggests that \(\sqrt{2}\) is a rational number, which contradicts Theorem 4.7.1. Explain the discrepancy.

Text Transcription:

sqrt 2

1.414213562 = 1414213562/1000000000

ANSWER:

Solution:Step 1:In this question we have to resolve the discrepancy of calculator display of resulting in rational representation and the actual value of without any rounding off.

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