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If (\sqrt{8}) is considered instead of (\sqrt{2}), what is the best short reason that (\sqrt{8}) is irrational?यदि (\sqrt{2}) की जगह (\sqrt{8}) पर विचार किया जाए, तो (\sqrt{8}) के अपरिमेय होने का सबसे सही छोटा तर्क क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\sqrt{8}=2\sqrt{2}), and multiplying irrational (\sqrt{2}) by nonzero rational (2) gives an irrational number(\sqrt{8}=2\sqrt{2}), और परिमेय (2) को अपरिमेय (\sqrt{2}) से गुणा करने पर अपरिमेय संख्या मिलती है
Step 1: (\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2}). Step 2: (\sqrt{2}) is irrational and (2) is a nonzero rational number, so (2\sqrt{2}) remains irrational. Step 3: Separate perfect-square factors while simplifying roots.चरण 1: (\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2})। चरण 2: (\sqrt{2}) अपरिमेय है और (2) शून्येतर परिमेय है, इसलिए (2\sqrt{2}) अपरिमेय रहेगा। चरण 3: सरलीकरण में पूर्ण वर्ग गुणनखंड अलग करें।
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