To determine which of the given numbers is irrational, we need to examine each of them:
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−1 5/29: This is a mixed number that can be converted to a simple fraction. The whole number part is -1, and the fractional part is \(\frac{5}{29}\). Combined, this gives: \[ -1 5/29 = -\frac{29}{29} - \frac{5}{29} = -\frac{34}{29} \] Since -34 and 29 are both integers, this is a rational number.
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0.343434...: This is a repeating decimal, which can be represented as a fraction. It can be expressed as: \[ 0.343434... = \frac{34}{99} \] Therefore, this is also a rational number.
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√2/3: The square root of 2, \(\sqrt{2}\), is known to be an irrational number. When you divide an irrational number by a rational number (in this case, 3), the result is still irrational. Therefore, \(\frac{\sqrt{2}}{3}\) is irrational.
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87.9821: This is a finite decimal, which can also be expressed as a fraction. Thus, it is a rational number.
Based on this analysis, the only irrational number among the options provided is:
√2/3.
3 answers