Question

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

52.781654292
52.781654292

3.6363636363636363...
3.6363636363636363...

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

−7 8/37

Answer 1

To determine which of the given numbers is irrational, let's evaluate each option:

1. **52.781654292**: This number is a finite decimal, which means it is rational.

2. **3.6363636363636363...**: This number has a repeating decimal (the "63" repeats), which means it is also rational.

3. **3√/4 (∛3/4)**: This expression represents the cube root of 3 divided by 4. The cube root of 3 is an irrational number, and since dividing an irrational number by a rational number (4) does not make it rational, this value is irrational.

4. **−7 8/37**: This is a mixed number that can be converted to an improper fraction. It is the same as \(-\frac{7 \times 37 + 8}{37} = -\frac{259}{37}\), which is a rational number.

Based on this analysis, the only irrational number among the options is **3√/4 (∛3/4)**.