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A student says, “The product of two irrational numbers is always irrational.” Which of the following examples proves that the statement is wrong?एक विद्यार्थी कहता है, “दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय होता है।” निम्नलिखित में से कौन-सा उदाहरण उसके कथन को गलत सिद्ध करता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\sqrt{2}\times\sqrt{8}=4\)\(\sqrt{2}\times\sqrt{8}=4\)
Both \(\sqrt{2}\) and \(\sqrt{8}\) are irrational, but \(\sqrt{2}\times\sqrt{8}=\sqrt{16}=4\), which is rational. Hence the word “always” makes the statement false. Exam tip: disprove universal claims using one counterexample.\(\sqrt{2}\) और \(\sqrt{8}\) दोनों अपरिमेय हैं, पर \(\sqrt{2}\times\sqrt{8}=\sqrt{16}=4\), जो परिमेय है। अतः “हमेशा” वाला कथन गलत है। परीक्षा में सार्वत्रिक कथन को एक प्रतिउदाहरण से जाँचें।
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