Question

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

−7837
negative 7 Start Fraction 8 over 37 End Fraction

3.6363636363636363...
3.6363636363636363...

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

52.781654292

Answer 1

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

1. **−7837**: This is an integer, and all integers are rational numbers.

2. **negative 7 Start Fraction 8 over 37 End Fraction**: This can be expressed as the fraction \(-7 - \frac{8}{37}\), which is also a rational number since it can be represented as a fraction of two integers.

3. **3.6363636363636363...**: This is a repeating decimal (the 36 repeats indefinitely). All repeating decimals are rational numbers.

4. **3√4 (cubed root of 4)**: The cube root of a number can be rational or irrational. Specifically, \(\sqrt[3]{4}\) is not a perfect cube, so it is not an integer. The value is approximately 1.5874, which cannot be expressed as a fraction of two integers, making this an irrational number.

5. **52.781654292**: This is a terminating decimal, and all terminating decimals are rational numbers.

Thus, the only irrational number from the options provided is **3√4 (or the cube root of 4)**.