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Amit claims that \(4\sqrt{3}\) is a rational number. Which argument correctly shows the error in his claim?अमित का दावा है कि \(4\sqrt{3}\) एक परिमेय संख्या है। उसके दावे की त्रुटि दिखाने वाला सही तर्क कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: If \(4\sqrt{3}\) were rational, dividing it by 4 would make \(\sqrt{3}\) rational, which is impossible.यदि \(4\sqrt{3}\) परिमेय हो, तो 4 से भाग देने पर \(\sqrt{3}\) परिमेय होगी, जो असंभव है।
Assume \(4\sqrt{3}\) is rational. Since 4 is a non-zero rational number, \((4\sqrt{3})/4=\sqrt{3}\) would also be rational, contradicting the fact that \(\sqrt{3}\) is irrational. Exam tip: division by a non-zero rational preserves rationality.मान लें \(4\sqrt{3}\) परिमेय है। 4 एक शून्येतर परिमेय संख्या है, अतः \((4\sqrt{3})/4=\sqrt{3}\) भी परिमेय होती, जो असत्य है। परीक्षा में याद रखें: शून्येतर परिमेय से भाग देने पर परिमेयता बनी रहती है।
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