Asked by hi √
Which of the following is irrational?(1 point)
Responses
3.636363636363636...
3.636363636363636...
52.781654292
52.781654292
√3/4
−7 8/37
Responses
3.636363636363636...
3.636363636363636...
52.781654292
52.781654292
√3/4
−7 8/37
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which number is irrational, let's analyze each option:
1. **3.636363636363636...** - This is a repeating decimal (3.63...) and can be expressed as a fraction, thus it is a rational number.
2. **52.781654292** - This is a non-repeating, finite decimal. Since it ends, it can also be expressed as a fraction, making it a rational number.
3. **√3/4** - The square root of 3 (√3) is an irrational number. Dividing an irrational number by a rational number (like 4) still results in an irrational number. Thus, √3/4 is irrational.
4. **−7 8/37** - This is a mixed number which can be expressed as a whole number and a fraction. It is also a rational number since it can be converted into an improper fraction.
Given this analysis, the only irrational number among the options is:
**√3/4**.
1. **3.636363636363636...** - This is a repeating decimal (3.63...) and can be expressed as a fraction, thus it is a rational number.
2. **52.781654292** - This is a non-repeating, finite decimal. Since it ends, it can also be expressed as a fraction, making it a rational number.
3. **√3/4** - The square root of 3 (√3) is an irrational number. Dividing an irrational number by a rational number (like 4) still results in an irrational number. Thus, √3/4 is irrational.
4. **−7 8/37** - This is a mixed number which can be expressed as a whole number and a fraction. It is also a rational number since it can be converted into an improper fraction.
Given this analysis, the only irrational number among the options is:
**√3/4**.
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