To determine which of the numbers listed is irrational, we need to look at each option:
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3.6363636363636363... - This number is a repeating decimal. Repeating decimals can be expressed as fractions, so they are rational.
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\( \frac{\sqrt{3}}{4} \) - The square root of 3 is an irrational number, and dividing an irrational number by a rational number (4) still results in an irrational number. Thus, \( \frac{\sqrt{3}}{4} \) is irrational.
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52.781654292 - This is a non-repeating, non-terminating decimal that appears to be a finite decimal. If it is finite (even if it's long), it is considered a rational number.
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−7837 - This is a whole number, which is also a rational number.
In conclusion, the only irrational number from the provided options is:
\( \frac{\sqrt{3}}{4} \).