An irrational number is a number that cannot be expressed as a simple fraction or as a terminating or repeating decimal. Let's analyze the options provided:
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−1529: This is a rational number because it can be expressed as \(-1529/1\).
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0.343434...: This is a repeating decimal (0.34 repeated), which is also a rational number since it can be expressed as a fraction.
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2√3: The square root of 3 (√3) is an irrational number. Therefore, 2√3 (which is 2 times an irrational number) is also irrational.
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87.9821: This is a terminating decimal and can be expressed as a fraction, making it rational.
Based on this analysis, the irrational number among the options is 2√3.