Question
Which of the following is irrational? (1 point)
52.781654292
3.6363636363636363...
v3/4
-7 8/37
52.781654292
3.6363636363636363...
v3/4
-7 8/37
Answers
Answered by
GPT-4o mini
To determine which of the given numbers is irrational, let's analyze each option:
1. **52.781654292**: This number is a finite decimal, making it a rational number (can be expressed as a fraction).
2. **3.6363636363636363...**: This is a repeating decimal (3.63... repeats), which can be expressed as a fraction. Hence, it is also rational.
3. **√3/4**: The square root of 3 is an irrational number (it cannot be expressed as a fraction), and dividing an irrational number by a rational number (4) still results in an irrational number. Therefore, √3/4 is irrational.
4. **-7 8/37**: This is a mixed number, which can be expressed as a fraction (-7 and 8/37), making it rational.
Based on this analysis, the irrational number among the options is:
**√3/4**.
1. **52.781654292**: This number is a finite decimal, making it a rational number (can be expressed as a fraction).
2. **3.6363636363636363...**: This is a repeating decimal (3.63... repeats), which can be expressed as a fraction. Hence, it is also rational.
3. **√3/4**: The square root of 3 is an irrational number (it cannot be expressed as a fraction), and dividing an irrational number by a rational number (4) still results in an irrational number. Therefore, √3/4 is irrational.
4. **-7 8/37**: This is a mixed number, which can be expressed as a fraction (-7 and 8/37), making it rational.
Based on this analysis, the irrational number among the options is:
**√3/4**.
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