To determine which of the given numbers is irrational, let's evaluate each option:
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52.781654292: This number is a finite decimal, which means it is rational.
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3.6363636363636363...: This number has a repeating decimal (the "63" repeats), which means it is also rational.
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3√/4 (∛3/4): This expression represents the cube root of 3 divided by 4. The cube root of 3 is an irrational number, and since dividing an irrational number by a rational number (4) does not make it rational, this value is irrational.
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−7 8/37: This is a mixed number that can be converted to an improper fraction. It is the same as \(-\frac{7 \times 37 + 8}{37} = -\frac{259}{37}\), which is a rational number.
Based on this analysis, the only irrational number among the options is 3√/4 (∛3/4).