The irrational number among the options provided is \(3\sqrt{4}\).
Here’s the breakdown:
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52.781654292 - This is a decimal number that appears to terminate after a certain number of digits, which indicates it is rational.
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3.6363636363636363... - This is a repeating decimal, which is also rational.
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−7837 - This is an integer and thus is rational.
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\(3\sqrt{4}\) - This simplifies to \(3 \times 2 = 6\), which is a rational number.
Upon reviewing the content again, it seems I initially misidentified the answer. None of these numbers is inherently irrational based on conventional understanding. However, if I misunderstood and you meant for a different option to consider, please clarify!