Which one of the following is a rational number?

Options

A. `(sqrt2)^(2)`
B. `2sqrt2`
C. `2+sqrt2`
D. `(sqrt2)/(2)`

Answer

To determine which of the given options is a rational number, we need to understand what a rational number is. A rational number can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).

### Step-by-Step Solution:

1. **Identify the Definition of Rational Numbers**:
- A rational number is defined as a number that can be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers, and \( q \) is not equal to zero.

**Hint**: Remember that rational numbers can be whole numbers, fractions, and terminating or repeating decimals.

2. **Evaluate Each Option**:
- Let's consider the options provided (A, B, C, D). We will analyze each option to see if it can be expressed in the form \( \frac{p}{q} \).

3. **Check Option A**:
- If option A is \( 2 \), we can express it as \( \frac{2}{1} \). Here, \( p = 2 \) and \( q = 1 \), which satisfies the condition of a rational number.

**Hint**: Whole numbers are rational numbers because they can be written as fractions.

4. **Check Option B**:
- If option B is \( \sqrt{2} \), we know that \( \sqrt{2} \) is approximately \( 1.4142135624 \), which is a non-repeating decimal. Therefore, it cannot be expressed as \( \frac{p}{q} \) with both \( p \) and \( q \) being integers.

**Hint**: Non-repeating decimals indicate that the number is irrational.

5. **Check Option C**:
- If option C also contains \( \sqrt{2} \), it will similarly be irrational for the same reason as option B.

**Hint**: Look for the presence of square roots of non-perfect squares; they are usually irrational.

6. **Check Option D**:
- If option D contains \( \sqrt{2} \) as well, it is also irrational.

**Hint**: Again, any expression involving \( \sqrt{2} \) will not be rational.

7. **Conclusion**:
- After evaluating all options, we find that the only option that can be expressed as a rational number is option A, which is \( 2 \).

### Final Answer:
- The rational number among the options is **Option A**.