Question

Question
Which of the following is irrational?(1 point)
Responses

3.6363636363636363...
3.6363636363636363...

−7 8/37
negative 7 Start Fraction 8 over 37 End Fraction

3√4
Start Fraction Start Root 3 End Root over 4 End Fraction

52.781654292

Answer 1

To determine which of the given options is irrational, we need to identify the nature of each option.

1. **3.6363636363636363...**: This is a repeating decimal, which can be expressed as the fraction \( \frac{109}{30} \). Therefore, it is rational.

2. **−7 8/37**: This is a mixed number, which can be expressed as \( -7 + \frac{8}{37} = -\frac{259}{37} \). Since it can be written as a fraction of two integers, it is rational.

3. **3√4** (interpreted as \( \frac{\sqrt{3}}{4} \)): The square root of 3 (√3) is an irrational number, and dividing an irrational number by a rational number (4) remains irrational. Thus, \( \frac{\sqrt{3}}{4} \) is irrational.

4. **52.781654292**: This is a decimal number that is not repeating, but it is a specific numerical value, which means it can be expressed as a fraction. Therefore, it is rational.

Based on this analysis, the option that is irrational is:

**3√4 (interpreted as \(\frac{\sqrt{3}}{4}\))**.