To determine which of the options is irrational, we will analyze each one:
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3.6363636363636363...: This is a repeating decimal. Any repeating decimal can be expressed as a fraction, therefore this number is rational.
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√3 over 4: The square root of 3 (√3) is an irrational number. Since the division of an irrational number by a non-zero rational number (4) remains irrational, √3/4 is irrational.
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−7 and 8 over 37: This notation seems to represent a mixed number, which can be written as \(-7 + \frac{8}{37}\). Both integers and fractions (like 8/37) are rational. Therefore, this expression is rational.
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52.781654292: This is a finite decimal, which can also be expressed as a fraction. Hence, this number is rational.
Based on the analysis, the option that is irrational is:
√3 over 4.