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A student claims that \(5+\sqrt{3}\) is rational because 5 is rational. Which is the correct refutation of this claim?एक विद्यार्थी कहता है कि \(5+\sqrt{3}\) परिमेय है, क्योंकि 5 परिमेय है। इस दावे का सही खंडन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: If \(5+\sqrt{3}\) were rational, subtracting 5 would make \(\sqrt{3}\) rational, which is impossible.यदि \(5+\sqrt{3}\) परिमेय होता, तो उसमें से 5 घटाने पर \(\sqrt{3}\) परिमेय होता, जो असंभव है।
Assume \(5+\sqrt{3}\) is rational. Subtracting 5 makes \(\sqrt{3}\) rational, a contradiction. Thus 5 being rational is insufficient. Exam tip: rationals are closed under subtraction.मान लें \(5+\sqrt{3}\) परिमेय है। 5 घटाने पर \(\sqrt{3}\) भी परिमेय होगा, जो विरोधाभास है। 5 का परिमेय होना पर्याप्त नहीं। टिप: परिमेय संख्याएँ घटाव के लिए बंद हैं।
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