Question

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

3.6363636363636363...
3.6363636363636363...

−7837
negative 7 Start Fraction 8 over 37 End Fraction

52.781654292
52.781654292

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

Answer 1

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

1. **3.6363636363636363...** - This is a repeating decimal and can be expressed as a fraction. Therefore, it is a rational number.

2. **−7837** - This is a whole number, and all whole numbers are rational. Hence, this is rational.

3. **52.781654292** - This is a decimal that does not repeat and is not a whole number. However, without further context, it's likely it is a rounded representation of some rational number, but we can't definitively say it is irrational just based on the decimal provided.

4. **3√4 / 4** - This expression represents \( \sqrt[3]{4} / 4 \). The cube root of 4 is not a perfect cube, which means it is an irrational number. Dividing an irrational number by a rational number (4) results in an irrational number.

Considering the above analysis, the expression **3√4 / 4** is irrational.