To determine which of the given options is irrational, we need to identify the nature of each option.
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3.6363636363636363...: This is a repeating decimal, which can be expressed as the fraction \( \frac{109}{30} \). Therefore, it is rational.
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−7 8/37: This is a mixed number, which can be expressed as \( -7 + \frac{8}{37} = -\frac{259}{37} \). Since it can be written as a fraction of two integers, it is rational.
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3√4 (interpreted as \( \frac{\sqrt{3}}{4} \)): The square root of 3 (√3) is an irrational number, and dividing an irrational number by a rational number (4) remains irrational. Thus, \( \frac{\sqrt{3}}{4} \) is irrational.
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52.781654292: This is a decimal number that is not repeating, but it is a specific numerical value, which means it can be expressed as a fraction. Therefore, it is rational.
Based on this analysis, the option that is irrational is:
3√4 (interpreted as \(\frac{\sqrt{3}}{4}\)).
1 answer