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A student calls \(\sqrt{2}\) irrational after seeing its decimal form 1.414213... . Which property must be proved to justify the conclusion?एक विद्यार्थी
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Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Non-terminating and non-repeatingअनंत और अनावर्ती
A rational number has a terminating or repeating decimal expansion. Hence \(\sqrt{2}\) must be non-terminating and non-repeating. Exam tip: many displayed digits alone are not proof.परिमेय संख्या का दशमलव प्रसार सांत या अनंत आवर्ती होता है। अतः \(\sqrt{2}\) के लिए अनंत अनावर्ती प्रसार जरूरी है। परीक्षा-टिप: केवल कई अंक दिखना प्रमाण नहीं।
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