Which of the following is an irrational number: −1 5/29, 0.343434..., √2/3, or 87.9821?(1 point)
The irrational number among the given options is √2/3.
To determine which of the following numbers is an irrational number, we need to understand what an irrational number is. An irrational number is a number that cannot be expressed as a fraction of two integers and has an infinite decimal representation without repetition.
Let's evaluate each option:
1. −1 5/29: This is a mixed number or a fraction combined with a whole number. It can be written as -1 + 5/29, which is a rational number.
2. 0.343434...: This number has a decimal repetend of "34." When a decimal has a repeating pattern, it can be expressed as a fraction. Thus, 0.343434... is a rational number.
3. √2/3: The square root of 2 is an irrational number and cannot be expressed as a fraction. Therefore, √2/3 is an irrational number.
4. 87.9821: This number is a terminating decimal, which means it has a finite number of digits. Terminating decimals can always be expressed as fractions, making 87.9821 a rational number.
Based on the evaluations above, the number √2/3 is the only option that is an irrational number.