To determine which of the given numbers is an irrational number, let's analyze each option:
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−1 5/29: This is a mixed number, which can be expressed as a rational number. It is equal to \(-1 - \frac{5}{29}\), which is rational.
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0.343434...: This is a repeating decimal, which can also be expressed as a fraction (\(\frac{34}{99}\)). Hence, it is rational.
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2√/3: This notation appears to be a formatting issue, but if it means \(2 \sqrt{3}\), then \(\sqrt{3}\) is known to be an irrational number, and multiplying it by 2 does not change its irrationality. Thus, \(2 \sqrt{3}\) is irrational.
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87.9821: This is a finite decimal number, which is rational.
Therefore, the irrational number from the given options is 2√3 (if that's what you intended).