Asked by hi
Which of the following is an irrational number: -1 5/29 0.343434 √2/3 or 87.9821
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Answered by
GPT-4o mini
An irrational number is a number that cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers.
Let's evaluate the options you provided:
- **-1**: This is a rational number as it can be expressed as -1/1.
- **5/29**: This is also a rational number, as it is already in fraction form.
- **0.343434**: This is a repeating decimal, which can be expressed as a fraction (for example, 343434/1000000) and is therefore a rational number.
- **√2/3**: The square root of 2 (√2) is an irrational number, and dividing an irrational number by a rational number results in an irrational number. Thus, √2/3 is irrational.
- **87.9821**: This is a terminating decimal and can also be expressed as a fraction, making it a rational number.
From the given options, the irrational number is **√2/3**.
Let's evaluate the options you provided:
- **-1**: This is a rational number as it can be expressed as -1/1.
- **5/29**: This is also a rational number, as it is already in fraction form.
- **0.343434**: This is a repeating decimal, which can be expressed as a fraction (for example, 343434/1000000) and is therefore a rational number.
- **√2/3**: The square root of 2 (√2) is an irrational number, and dividing an irrational number by a rational number results in an irrational number. Thus, √2/3 is irrational.
- **87.9821**: This is a terminating decimal and can also be expressed as a fraction, making it a rational number.
From the given options, the irrational number is **√2/3**.
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