Question

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

3.6363636363636363...
3.6363636363636363...

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

52.781654292
52.781654292

−7837

Answer 1

To determine which of the numbers listed is irrational, we need to look at each option:

1. **3.6363636363636363...** - This number is a repeating decimal. Repeating decimals can be expressed as fractions, so they are rational.

2. **\( \frac{\sqrt{3}}{4} \)** - The square root of 3 is an irrational number, and dividing an irrational number by a rational number (4) still results in an irrational number. Thus, \( \frac{\sqrt{3}}{4} \) is irrational.

3. **52.781654292** - This is a non-repeating, non-terminating decimal that appears to be a finite decimal. If it is finite (even if it's long), it is considered a rational number.

4. **−7837** - This is a whole number, which is also a rational number.

In conclusion, the only irrational number from the provided options is:

**\( \frac{\sqrt{3}}{4} \)**.