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Which of the following numbers can be proved irrational using its prime factorisation?निम्नलिखित में से किस संख्या को उसके अभाज्य गुणनखंडों के आधार पर अपरिमेय सिद्ध किया जा सकता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\sqrt{3}\)\(\sqrt{3}\)
\(\sqrt{3}\) is irrational because 3 is not a perfect square: its prime factor 3 has exponent 1, which is odd. In contrast, \(\sqrt{9}=3\) is rational. Exam tip: a perfect square has only even prime exponents.\(\sqrt{3}\) अपरिमेय है, क्योंकि 3 पूर्ण वर्ग नहीं है; इसका अभाज्य गुणनखंड 3 की घात 1 है, जो विषम है। \(\sqrt{9}=3\) परिमेय है। परीक्षा में जाँचें कि सभी घातें सम हैं या नहीं।
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