To determine which of the given numbers is irrational, we need to identify if they can be expressed as a fraction of two integers (a rational number).
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52.781654292 - This is a decimal number and can be represented as a fraction, therefore it is rational.
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−7837 - This is an integer and can be represented as a fraction (−7837/1), so it is rational.
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3.6363636363636363... - This is a repeating decimal (3.63...), which can also be expressed as a fraction. Therefore, it is rational.
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√3/4 - The square root of 3 is an irrational number. Since an irrational number divided by a rational number (4) is still irrational, √3/4 is also irrational.
Thus, the only irrational number among the choices is √3/4.