Given an example of number x such that `x` is an irrational number and `x^(3)` is a rational number .

Answer

To find an example of a number \( x \) such that \( x \) is an irrational number and \( x^3 \) is a rational number, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Irrational Numbers**:
- An irrational number is a number that cannot be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).

2. **Identify a Suitable Irrational Number**:
- We need to find an irrational number \( x \) such that when we cube it, the result \( x^3 \) is a rational number.

3. **Choose \( x \) as the Cube Root of a Rational Number**:
- Let's take \( x = \sqrt[3]{5} \).
- Here, \( \sqrt[3]{5} \) is an irrational number because 5 is not a perfect cube.

4. **Calculate \( x^3 \)**:
- Now, we calculate \( x^3 \):
\[ x^3 = \left(\sqrt[3]{5}\right)^3 = 5 \]
- The result, 5, is a rational number since it can be expressed as \( \frac{5}{1} \).

5. **Conclusion**:
- Therefore, we have found that \( x = \sqrt[3]{5} \) is an irrational number, and \( x^3 = 5 \) is a rational number.

### Final Answer:
An example of a number \( x \) such that \( x \) is an irrational number and \( x^3 \) is a rational number is:
\[ x = \sqrt[3]{5} \]