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A calculator displays \(\sqrt{3}\) as 1.732. Mohan concludes that \(\sqrt{3}\) is rational. What is Mohan’s error?एक कैलकुलेटर
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Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: A calculator shows only an approximate decimal value; 1.732 is not the exact value of \(\sqrt{3}\).कैलकुलेटर केवल सन्निकट दशमलव मान दिखाता है; 1.732, \(\sqrt{3}\) का सटीक मान नहीं है।
A calculator gives a rounded approximation, so 1.732 is not the exact value of \(\sqrt{3}\). For proof, assume \(\sqrt{3}=a/b\) in lowest terms and derive a contradiction. Exam tip: never use a displayed decimal as proof of rationality.कैलकुलेटर सीमित अंकों तक सन्निकट मान देता है, इसलिए 1.732 को \(\sqrt{3}\) का सटीक मान नहीं मान सकते। प्रमाण में \(\sqrt{3}=a/b\) मानकर विरोधाभास दिखाते हैं। परीक्षा में अनुमानित दशमलव से परिमेयता सिद्ध न करें।
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