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On positive real numbers, (a*b=\sqrt{ab}) is defined. Is this operation commutative?धनात्मक वास्तविक संख्याओं पर (a*b=\sqrt{ab}) परिभाषित है। क्या यह संक्रिया क्रमविनिमेय है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Yesहाँ
Step 1: Write (a*b=\sqrt{ab}) and (b*a=\sqrt{ba}). Step 2: Since (ab=ba), both square roots are equal. Step 3: Use the commutative property of multiplication to test the new operation.चरण 1: (a*b=\sqrt{ab}) और (b*a=\sqrt{ba}) लिखें। चरण 2: क्योंकि (ab=ba), दोनों का वर्गमूल समान होगा। चरण 3: गुणन के क्रमविनिमेय गुण का प्रयोग करके नई संक्रिया की जांच करें।
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