To determine which of the given numbers is irrational, let's analyze each option:
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−7837: This is an integer, and all integers are rational numbers.
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negative 7 Start Fraction 8 over 37 End Fraction: This can be expressed as the fraction \(-7 - \frac{8}{37}\), which is also a rational number since it can be represented as a fraction of two integers.
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3.6363636363636363...: This is a repeating decimal (the 36 repeats indefinitely). All repeating decimals are rational numbers.
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3√4 (cubed root of 4): The cube root of a number can be rational or irrational. Specifically, \(\sqrt[3]{4}\) is not a perfect cube, so it is not an integer. The value is approximately 1.5874, which cannot be expressed as a fraction of two integers, making this an irrational number.
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52.781654292: This is a terminating decimal, and all terminating decimals are rational numbers.
Thus, the only irrational number from the options provided is 3√4 (or the cube root of 4).
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