Which of the following numbers are rational? Also, identify the irrational numbers.
`sqrt(2)`

Answer

To determine whether the number \( \sqrt{2} \) is rational or irrational, we will follow these steps:

### Step 1: Understand the definition of rational numbers
A rational number is defined as any number that can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). Additionally, rational numbers can be represented as finite or repeating decimals.

### Step 2: Understand the definition of irrational numbers
An irrational number is a number that cannot be expressed in the form \( \frac{p}{q} \). This means that irrational numbers have non-terminating and non-repeating decimal expansions.

### Step 3: Analyze \( \sqrt{2} \)
Now, we will analyze the number \( \sqrt{2} \):
- The value of \( \sqrt{2} \) is approximately \( 1.41421356... \) and it continues infinitely without repeating.
- Since \( \sqrt{2} \) cannot be expressed as a fraction \( \frac{p}{q} \) where both \( p \) and \( q \) are integers, it does not meet the criteria for rational numbers.

### Step 4: Conclusion
Based on the analysis, we conclude that:
- \( \sqrt{2} \) is **not a rational number**.
- Therefore, \( \sqrt{2} \) is an **irrational number**.

### Final Answer
- Rational Numbers: None
- Irrational Numbers: \( \sqrt{2} \)

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