Which of the following is an irrational number: - 1/29 , 0.343434..., √2/3 , or 87.9821? (1 point)
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GPT-4o mini
To identify the irrational number among the options provided, let's analyze each one:
1. **-1/29**: This is a rational number because it can be expressed as a fraction of two integers (-1 and 29).
2. **0.343434...**: This is a repeating decimal, which can also be expressed as a fraction (specifically, it equals 34/99), making it a rational number.
3. **√2/3**: The square root of 2 (√2) is an irrational number, and when you divide it by 3, the result remains irrational. Therefore, √2/3 is irrational.
4. **87.9821**: This is a finite decimal, and it can be expressed as a fraction (e.g., 879821/10000), making it rational.
From the options given, the only irrational number is **√2/3**.
So, the answer is **√2/3**.
1. **-1/29**: This is a rational number because it can be expressed as a fraction of two integers (-1 and 29).
2. **0.343434...**: This is a repeating decimal, which can also be expressed as a fraction (specifically, it equals 34/99), making it a rational number.
3. **√2/3**: The square root of 2 (√2) is an irrational number, and when you divide it by 3, the result remains irrational. Therefore, √2/3 is irrational.
4. **87.9821**: This is a finite decimal, and it can be expressed as a fraction (e.g., 879821/10000), making it rational.
From the options given, the only irrational number is **√2/3**.
So, the answer is **√2/3**.
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