Question

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

3.636363636363636...
3.636363636363636...

52.781654292
52.781654292

√3/4

−7 8/37

Answer 1

To determine which number is irrational, let's analyze each option:

1. **3.636363636363636...** - This is a repeating decimal (3.63...) and can be expressed as a fraction, thus it is a rational number.

2. **52.781654292** - This is a non-repeating, finite decimal. Since it ends, it can also be expressed as a fraction, making it a rational number.

3. **√3/4** - The square root of 3 (√3) is an irrational number. Dividing an irrational number by a rational number (like 4) still results in an irrational number. Thus, √3/4 is irrational.

4. **−7 8/37** - This is a mixed number which can be expressed as a whole number and a fraction. It is also a rational number since it can be converted into an improper fraction.

Given this analysis, the only irrational number among the options is:

**√3/4**.