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A student says, “\(\sqrt{3}\) is rational because it can be written as \(1.732\).” What is the main flaw in this reasoning?एक विद्यार्थी कहता है, “\(\sqrt{3}\) परिमेय है, क्योंकि इसे \(1.732\) के रूप में लिखा जा सकता है।” इस तर्क की मुख्य त्रुटि क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Treating \(1.732\) as an exact value is wrong; it is only an approximation.\(1.732\) को सटीक मान मानना गलत है; यह केवल सन्निकट मान है।
Because \(1.732^2=2.999824\ne3\), 1.732 is an approximation, not the exact value. A decimal point does not make a number irrational. Exam tip: square a claimed exact value.\(1.732^2=2.999824\ne3\), इसलिए 1.732 केवल सन्निकट मान है, सटीक नहीं। दशमलव बिंदु से संख्या अपरिमेय नहीं होती। परीक्षा में दावे को वर्ग करके जाँचें।
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