Rima says that \(5+\sqrt{2}\) is a rational number because 5 is rational. Which is the correct evaluation of her statement?रीमा कहती है कि \(5+\sqrt{2}\) परिमेय संख्या है, क्योंकि 5 परिमेय है। उसके कथन का सही मूल्यांकन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: The statement is incorrect; if \(5+\sqrt{2}\) were rational, subtracting 5 would make \(\sqrt{2}\) rational too.कथन गलत है; यदि \(5+\sqrt{2}\) परिमेय होता, तो उसमें से 5 घटाने पर \(\sqrt{2}\) भी परिमेय होता।
\(\sqrt{2}\) is irrational. If \(5+\sqrt{2}\) were rational, subtracting the rational number 5 would make \(\sqrt{2}\) rational, a contradiction. Hence the sum is irrational. Exam tip: isolate the irrational term by adding or subtracting a rational number.\(\sqrt{2}\) अपरिमेय है। मान लें \(5+\sqrt{2}\) परिमेय है; तब उसमें से परिमेय 5 घटाने पर \(\sqrt{2}\) परिमेय निकलता, जो विरोधाभास है। अतः योग अपरिमेय है। परीक्षा टिप: विरोधाभास के लिए परिमेय पद को अलग करें।
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