Question

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

52.781654292
52.781654292

−7837
negative 7 Start Fraction 8 over 37 End Fraction

3.6363636363636363...
3.6363636363636363...

√3/4

Answer 1

To determine which of the given numbers is irrational, we need to identify if they can be expressed as a fraction of two integers (a rational number).

1. **52.781654292** - This is a decimal number and can be represented as a fraction, therefore it is rational.

2. **−7837** - This is an integer and can be represented as a fraction (−7837/1), so it is rational.

3. **3.6363636363636363...** - This is a repeating decimal (3.63...), which can also be expressed as a fraction. Therefore, it is rational.

4. **√3/4** - The square root of 3 is an irrational number. Since an irrational number divided by a rational number (4) is still irrational, √3/4 is also irrational.

Thus, the only irrational number among the choices is **√3/4**.