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
52.781654292

Answer 1

To determine which of the given responses is irrational, let's analyze each option:

1. **\( \sqrt[3]{4} \)**: The cube root of 4 is an irrational number since it cannot be expressed as a fraction of two integers.

2. **\( 3.6363636363636363... \)**: This is a repeating decimal (that can be expressed as \( \frac{11}{3} \)), which is a rational number.

3. **\( -7837 \frac{8}{37} \)**: This is a rational number since both the integer part (-7837) and the fractional part (\( \frac{8}{37} \)) can be expressed as a fraction.

4. **\( 52.781654292 \)**: This is a finite decimal and can be represented as a fraction, so it is also a rational number.

Based on this analysis, the irrational number among the options is:

- **\( \sqrt[3]{4} \)**.