Which of the following is not a rational number?

Options

A. `sqrt(2)`
B. `sqrt(4)`
C. `sqrt(9)`
D. `sqrt(25)`

Answer

To determine which of the following numbers is not a rational number, we need to analyze each option provided. A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Let's evaluate the options step by step:

1. **Option A: √2**
- The square root of 2 is an irrational number. It cannot be expressed as a fraction of two integers. Its decimal representation is approximately 1.41421, which is non-repeating and non-terminating.
- **Conclusion**: √2 is not a rational number.

2. **Option B: √4**
- The square root of 4 is 2 (since 2 × 2 = 4). The number 2 can be expressed as a fraction (2/1), which makes it a rational number.
- **Conclusion**: √4 is a rational number.

3. **Option C: √9**
- The square root of 9 is 3 (since 3 × 3 = 9). The number 3 can also be expressed as a fraction (3/1), making it a rational number.
- **Conclusion**: √9 is a rational number.

4. **Option D: √25**
- The square root of 25 is 5 (since 5 × 5 = 25). The number 5 can be expressed as a fraction (5/1), which makes it a rational number.
- **Conclusion**: √25 is a rational number.

**Final Answer**: The only number that is not a rational number among the options is **Option A: √2**.