To determine which of the options is irrational, let’s analyze each one:
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3.6363636363636363...: This number can be expressed as the fraction \( \frac{363636...}{100000...} \). This is a repeating decimal, which is equivalent to the fraction \( \frac{11}{3} \). Therefore, it is rational.
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3√4: This represents \( \sqrt[3]{4} \). The cube root of 4 cannot be expressed as a fraction of two integers, and therefore it is an irrational number.
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−7 and 8 over 37: This seems to be a misinterpretation; likely it refers to \( -7 + \frac{8}{37} \). Both \(-7\) and \(\frac{8}{37}\) are rational numbers, and the sum of two rational numbers is also rational. Thus, this option is rational.
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52.781654292: This is a finite decimal and can be expressed as a fraction, so it is rational.
Based on the analysis:
The irrational number among the options is \( 3\sqrt{4} \).
1 answer