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If \(x\) is an irrational number and \(r\) is a non-zero rational number, what type of number must \(rx\) be?यदि \(x\) एक अपरिमेय संख्या है और \(r\) शून्येतर परिमेय संख्या है, तो \(rx\) किस प्रकार की संख्या अवश्य होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Irrationalअपरिमेय
Assume \(rx\) is rational. Since \(r\ne0\) is rational, \(x=(rx)/r\) would also be rational, giving a contradiction. Hence \(rx\) is irrational. In exams, always check that the rational multiplier is non-zero.मान लें \(rx\) परिमेय है। चूँकि \(r\ne0\) परिमेय है, इसलिए \(x=(rx)/r\) भी परिमेय होगा, जो विरोधाभास है। अतः \(rx\) अपरिमेय है। परीक्षा में शून्येतर शर्त अवश्य जाँचें।
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