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Reema says, “\(\sqrt{3}\approx1.732\); therefore, \(\sqrt{3}\) is rational because 1.732 is rational.” What is the correct evaluation of Reema’s argument?रीमा कहती है, “\(\sqrt{3}\approx1.732\) है; अतः \(\sqrt{3}\) परिमेय संख्या है, क्योंकि 1.732 परिमेय है।” रीमा के तर्क की सही समीक्षा क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 1.732 is an approximation; its rationality does not prove that \(\sqrt{3}\) is rational1.732 एक सन्निकटन है; इसका परिमेय होना \(\sqrt{3}\) के परिमेय होने को सिद्ध नहीं करता
1.732 is a terminating rational approximation, not \(\sqrt{3}\) itself. Check: \(1.732^2=2.999824\), not 3. Exam tip: distinguish an approximate value from an exact value.1.732 एक समाप्त दशमलव वाला परिमेय सन्निकटन है, स्वयं \(\sqrt{3}\) नहीं। जाँचें: \(1.732^2=2.999824\), 3 नहीं। परीक्षा में सन्निकटन और ठीक मान अलग रखें।
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