Question

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

3.6363636363636363...
3.6363636363636363...

52.781654292
52.781654292

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

−7837
negative 7 Start Fraction 8 over 37 End Fraction

Answer 1

To determine which of the given numbers is irrational, we need to analyze each option:

1. **3.6363636363636363...** - This is a repeating decimal (specifically, it repeats the "63" indefinitely). Repeating decimals can be expressed as fractions, which means they are rational numbers.

2. **52.781654292** - This is a non-repeating decimal. However, non-repeating decimals can either be rational or irrational. In this case, it is a finite decimal, which can also be expressed as a fraction. Therefore, it is rational.

3. **3√4** - This notation seems to intend to represent the cube root of 4. The cube root of 4 is approximately 1.5874, and since it cannot be expressed as a fraction of two integers, it is considered an irrational number.

4. **−7837** - This is a whole number, and all integers are rational numbers.

Now, looking at the options, **3√4 (or the cube root of 4)** is the only irrational number among the choices provided.

So, the answer is:

**3√4** (cube root of 4).