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A student claims that \(\sqrt{2}\) is rational because \(1.414=\frac{1414}{1000}\). What is the main error in the argument?एक विद्यार्थी कहता है कि
\(\sqrt{2}\) परिमेय है क्योंकि \(1.414=\frac{1414}{1000}\) है। उसके तर्क में मुख्य त्रुटि क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\frac{1414}{1000}\) is only an approximation of \(\sqrt{2}\); its square is not exactly \(2\).\(\frac{1414}{1000}\), \(\sqrt{2}\) का केवल सन्निकट मान है; इसका वर्ग ठीक \(2\) नहीं है।
\(1.414\) is only an approximation, not the exact value of \(\sqrt{2}\). Check: \((1.414)^2=1.999396\), not \(2\). In exams, always distinguish an approximate decimal from an exact value.\(1.414\) केवल \(\sqrt{2}\) का सन्निकट मान है, बराबर नहीं। जाँचें: \((1.414)^2=1.999396\), जो \(2\) नहीं है। परीक्षा में सन्निकट और सटीक मान में अंतर अवश्य देखें।
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