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Let \(r\) be a rational number. Which statement about \(r+\sqrt{2}\) is always true?मान लें कि \(r\) कोई परिमेय संख्या है। संख्या \(r+\sqrt{2}\) के बारे में कौन-सा कथन सदैव सत्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Always irrationalसदैव अपरिमेय
Option B is correct. If \(r+\sqrt{2}\) were rational, subtracting the rational number \(r\) would make \(\sqrt{2}\) rational, which is impossible. Exam tip: rational ± irrational is always irrational.सही उत्तर B है। यदि \(r+\sqrt{2}\) परिमेय होता, तो उसमें से परिमेय \(r\) घटाने पर \(\sqrt{2}\) परिमेय मिलता, जो असंभव है। परीक्षा-टिप: परिमेय ± अपरिमेय सदैव अपरिमेय होता है।
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