To determine which of the provided numbers is irrational, let's analyze each one:
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−1 5/29 - This is a mixed number and can be converted into a proper 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. It can be expressed as the fraction \(\frac{34}{99}\), which is rational.
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√2/3 - The square root of 2 (\(\sqrt{2}\)) is an irrational number. Dividing an irrational number by a rational number (3) still results in an irrational number. Therefore, \(\sqrt{2}/3\) is irrational.
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87.9821 - This is a finite decimal, and it can be expressed as a fraction, making it a rational number.
Among the options, the irrational number is √2/3.
3 answers