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If \(r\) is a non-zero rational number, which statement about \(r\sqrt{3}\) is correct?यदि \(r\) कोई अशून्य परिमेय संख्या है, तो \(r\sqrt{3}\) के बारे में कौन-सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is always irrational.यह सदैव अपरिमेय होता है
If \(r\sqrt{3}=q\) were rational, then since \(r\ne0\), \(\sqrt{3}=q/r\) would also be rational, a contradiction. Thus A is correct. Tip: a non-zero rational multiplier preserves irrationality.यदि \(r\sqrt{3}=q\) परिमेय होता, तो \(r\ne0\) होने से \(\sqrt{3}=q/r\) भी परिमेय होता; यह विरोधाभास है। अतः A सही है। टिप: अशून्य परिमेय गुणक से अपरिमेयता बनी रहती है।
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