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A student says, “\(\sqrt{3}=1.732\), so \(\sqrt{3}\) is a rational number.” What is the main error in this statement?एक विद्यार्थी कहता है, “\(\sqrt{3}=1.732\) है, इसलिए \(\sqrt{3}\) परिमेय संख्या है।” इस कथन में मुख्य त्रुटि क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(1.732\) is only an approximation of \(\sqrt{3}\), not its exact value\(1.732\), \(\sqrt{3}\) का केवल सन्निकट मान है, उसका ठीक मान नहीं
\(1.732\) is a terminating decimal and hence rational, but it is only an approximation to \(\sqrt{3}\). Check: \(1.732^2=2.999824\), not \(3\). In exams, carefully distinguish an exact equality from an approximation.\(1.732\) एक समाप्त दशमलव है, इसलिए वह परिमेय है; पर यह \(\sqrt{3}\) का केवल सन्निकट मान है। जाँचें: \(1.732^2=2.999824\), जो \(3\) नहीं है। परीक्षा में “=” और “लगभग” के अंतर पर ध्यान दें।
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