To determine which of the given numbers is irrational, let's analyze each one:
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1 5/29: This is a mixed number that can be expressed as a fraction (1 + 5/29 = 34/29). Since it can be written as a ratio of two integers, it is a rational number.
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0.343434: This is a repeating decimal (0.343434...) which can also be expressed as a fraction (its exact form would be 34/99). Therefore, it is a rational number.
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√2/3: The square root of 2 (√2) is known to be an irrational number. Dividing an irrational number by a rational number (3, in this case) results in an irrational number. Therefore, √2/3 is irrational.
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87.9821: This is a finite decimal, which can be expressed as a fraction (879821/10000). Thus, it is a rational number.
The only irrational number from the provided choices is √2/3.
3 answers