To determine which of the options is irrational, we can analyze each one:
A) \(-7 \frac{8}{37}\) - This is a rational number because it can be expressed as a fraction \(-7 + \frac{8}{37} = -\frac{259}{37}\), which is a ratio of two integers.
B) \(3.6363636363636363...\) - This is also a rational number because it is a repeating decimal, which can be converted into a fraction.
C) \(52.781654292\) - This is a decimal representation and appears to be a non-repeating decimal. However, as long as it is a finite decimal or can be expressed as a fraction, it is rational. Since this number has a finite decimal representation, it is rational.
D) \(\frac{\sqrt{3}}{4}\) - The square root of 3 (\(\sqrt{3}\)) is known to be an irrational number. Since the division of an irrational number (numerator) by a rational number (denominator) results in an irrational number, \(\frac{\sqrt{3}}{4}\) is irrational.
Thus, the answer is D - \(\frac{\sqrt{3}}{4}\) is irrational.
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