Let's analyze the options provided to determine which one is irrational.
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52.781654292: This is a decimal number that terminates, therefore it is a rational number.
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52.781654292 - 7/8: This is the result of subtracting a rational number from a rational number, which will still yield a rational number.
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-7: This is an integer and hence a rational number.
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8/37: This is a fraction of two integers and is therefore a rational number.
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-3.6363636363636363...: This represents a repeating decimal (specifically, it could be interpreted as -3.636... or -3.63 with the 63 repeating). Repeating decimals are rational numbers.
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3√/4 (which I assume means \(\sqrt{3}/4\)): Here, \(\sqrt{3}\) is an irrational number (since it cannot be expressed as a fraction of two integers). Dividing an irrational number by a rational number (in this case, 4) results in an irrational number.
Therefore, the correct choice is:
- \(\sqrt{3}/4\) is the only option that is irrational.