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Rima says, “\(\sqrt{3}=1.732\); therefore, \(\sqrt{3}\) is rational.” What is the main error in her reasoning?रीमा कहती है, “\(\sqrt{3}=1.732\), इसलिए \(\sqrt{3}\) परिमेय है।” उसके तर्क की मुख्य त्रुटि क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: She has treated an approximation as an exact value.उसने सन्निकट मान को ठीक मान मान लिया है
\(1.732\) is only an approximation of \(\sqrt{3}\), not its exact value, since \(1.732^2=2.999824\), not 3. As 3 is not a perfect square, \(\sqrt{3}\) is irrational. Exam tip: always distinguish \(=\) from \(\approx\).\(1.732\), \(\sqrt{3}\) का केवल सन्निकट मान है, ठीक मान नहीं; क्योंकि \(1.732^2=2.999824\), जो 3 नहीं है। 3 पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{3}\) अपरिमेय है। परीक्षा टिप: \(=\) और \(\approx\) का अंतर अवश्य पहचानें।
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