An irrational number is a number that cannot be expressed as a fraction of two integers. Let's analyze the given numbers:
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−1 5/29: This is a mixed number that can be converted to an improper fraction: \[ -1 \frac{5}{29} = -\frac{29}{29} - \frac{5}{29} = -\frac{34}{29} \] This is a rational number.
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0.343434...: This is a repeating decimal, which can be expressed as a fraction (specifically, \(\frac{34}{99}\)). Hence, it is a rational number.
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2√3: The square root of 3 (\(\sqrt{3}\)) is known to be an irrational number. Multiplying it by 2: \[ 2 \times \sqrt{3} \] remains irrational, since the product of a rational number (2) and an irrational number (\(\sqrt{3}\)) is also irrational.
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87.9821: This is a terminating decimal, which can also be expressed as a fraction (e.g., \(\frac{879821}{10000}\)). Therefore, this is a rational number.
Based on this analysis, the irrational number from the list is:
2√3.
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