To determine which of the given numbers is irrational, let's analyze each option:
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−1529: This is a whole number and is therefore a rational number (it can be expressed as the fraction \(-1529/1\)).
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0.343434...: This is a repeating decimal, which can be expressed as the fraction \(\frac{34}{99}\). Therefore, it is also a rational number.
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\(2\sqrt{3}\): The square root of 3 (\(\sqrt{3}\)) is known to be an irrational number. Multiplying an irrational number (\(\sqrt{3}\)) by a rational number (2) results in an irrational number. Thus, \(2\sqrt{3}\) is irrational.
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87.9821: This is a finite decimal and can be expressed as the fraction \(\frac{879821}{10000}\), making it a rational number.
Based on the analysis, the irrational number among the options is:
\(2\sqrt{3}\).
1 answer