To determine which number is irrational, let's analyze each option:
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3.636363636363636... - This is a repeating decimal (3.63...) and can be expressed as a fraction, thus it is a rational number.
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52.781654292 - This is a non-repeating, finite decimal. Since it ends, it can also be expressed as a fraction, making it a rational number.
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√3/4 - The square root of 3 (√3) is an irrational number. Dividing an irrational number by a rational number (like 4) still results in an irrational number. Thus, √3/4 is irrational.
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−7 8/37 - This is a mixed number which can be expressed as a whole number and a fraction. It is also a rational number since it can be converted into an improper fraction.
Given this analysis, the only irrational number among the options is:
√3/4.
1 answer