To identify which of the given numbers is irrational, let's examine each option:
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52.781654292: This is a decimal number with a finite number of decimal places, hence it is a rational number.
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3.6363636363636363...: This number is a repeating decimal (3.6363...), which indicates it can be expressed as a fraction, thus it is a rational number.
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\(\frac{\sqrt{3}}{4}\): The square root of 3 is an irrational number, and dividing an irrational number by a non-zero rational number (4) results in an irrational number. Therefore, \(\frac{\sqrt{3}}{4}\) is irrational.
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−7 8/37: This is a mixed number, which can be expressed as \(-7 - \frac{8}{37}\). Since both integers and fractions are rational numbers, this represents a rational number.
Based on the analysis, the option that is irrational is:
\(\frac{\sqrt{3}}{4}\).
1 answer