To determine which of the given numbers is irrational, let's analyze each option:
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52.781654292 - This is a decimal that terminates and is therefore rational.
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3.6363636363636363... - This is a repeating decimal (3.63 with the "63" repeating), which is also rational.
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−7837 - This is an integer and therefore rational.
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3√4 - This can be simplified. The cube root of 4 (3√4) is approximately 1.5874010519681994, which cannot be expressed as a fraction of two integers; thus, it is irrational.
Therefore, the irrational number among the options is 3√4.