Question

Which of the following is irrational?(1 point) Responses 3√4 Start Fraction Start Root 3 End Root over 4 End Fraction 3.6363636363636363... 3.6363636363636363... −7837 negative 7 Start Fraction 8 over 37 End Fraction 52.781654292

Please simplify

Answer 1

To identify which of the given options is irrational, let's analyze each of them:

1. **\( \sqrt{4} \)**: This equals 2, which is a rational number.

2. **\( \frac{\sqrt{3}}{4} \)**: Here, \( \sqrt{3} \) is an irrational number, and dividing an irrational number by a non-zero rational number results in an irrational number. Thus, \( \frac{\sqrt{3}}{4} \) is irrational.

3. **3.6363636363636363...**: This represents a repeating decimal (3.63 with the "63" repeating). Repeating decimals are rational numbers. Thus, this is a rational number.

4. **−7837**: This is an integer, which is a rational number.

5. **\( \frac{8}{37} \)**: This is a fraction of two integers, so it is a rational number.

6. **52.781654292**: This is a finite decimal number, which is also a rational number.

From the analysis, **\( \frac{\sqrt{3}}{4} \)** is the only irrational number among the given options.