To determine which of the provided numbers is irrational, let's analyze each option:
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3.6363636363636363... - This is a repeating decimal and can be expressed as a fraction. Therefore, it is a rational number.
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−7837 - This is a whole number, and all whole numbers are rational. Hence, this is rational.
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52.781654292 - This is a decimal that does not repeat and is not a whole number. However, without further context, it's likely it is a rounded representation of some rational number, but we can't definitively say it is irrational just based on the decimal provided.
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3√4 / 4 - This expression represents \( \sqrt[3]{4} / 4 \). The cube root of 4 is not a perfect cube, which means it is an irrational number. Dividing an irrational number by a rational number (4) results in an irrational number.
Considering the above analysis, the expression 3√4 / 4 is irrational.