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Which option is correct for comparing (\sqrt{2}+\sqrt{18}) and (\sqrt{8}+\sqrt{12})?कौन सा विकल्प (\sqrt{2}+\sqrt{18}) और (\sqrt{8}+\sqrt{12}) की तुलना के लिए सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: The first is greaterपहला बड़ा है
Step 1: (\sqrt{2}+\sqrt{18}=4\sqrt{2}). Step 2: (\sqrt{8}+\sqrt{12}=2\sqrt{2}+2\sqrt{3}). Since (\sqrt{3}>\sqrt{2}), the second expression is greater. Step 3: Simplify first and compare carefully.चरण 1: (\sqrt{2}+\sqrt{18}=\sqrt{2}+3\sqrt{2}=4\sqrt{2})। चरण 2: (\sqrt{8}+\sqrt{12}=2\sqrt{2}+2\sqrt{3})। तुलना में (4\sqrt{2}) लगभग (5.66) और दूसरा लगभग (6.29) लगता है लेकिन शुद्ध तुलना में (2\sqrt{2}) और (2\sqrt{3}) के कारण दूसरा बड़ा है। चरण 3: अनुमान और सरल रूप दोनों जांचें।
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