Question

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

52.781654292

3.6363636363636363...

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

−7 8/37

Answer 1

To identify which of the given numbers is irrational, let's examine each option:

1. **52.781654292**: This is a decimal number with a finite number of decimal places, hence it is a rational number.

2. **3.6363636363636363...**: This number is a repeating decimal (3.6363...), which indicates it can be expressed as a fraction, thus it is a rational number.

3. **\(\frac{\sqrt{3}}{4}\)**: The square root of 3 is an irrational number, and dividing an irrational number by a non-zero rational number (4) results in an irrational number. Therefore, \(\frac{\sqrt{3}}{4}\) is irrational.

4. **−7 8/37**: This is a mixed number, which can be expressed as \(-7 - \frac{8}{37}\). Since both integers and fractions are rational numbers, this represents a rational number.

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

**\(\frac{\sqrt{3}}{4}\)**.