Which of the following is an irrational number?

Options

A. `sqrt9`
B. `sqrt11`
C. `(2)/(5)`
D. `(2)/(3)`

Answer

To determine which of the given options is an irrational number, we need to analyze each option based on the definition of irrational numbers. An irrational number cannot be expressed in the form of \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).

### Step-by-Step Solution:

1. **Examine Option 1: \( \sqrt{9} \)**
- Calculate \( \sqrt{9} \).
- \( \sqrt{9} = 3 \).
- Since 3 can be expressed as \( \frac{3}{1} \), it is a rational number.

2. **Examine Option 2: \( \sqrt{11} \)**
- \( \sqrt{11} \) is a prime number and cannot be simplified further.
- It cannot be expressed in the form \( \frac{p}{q} \) where both \( p \) and \( q \) are integers.
- Therefore, \( \sqrt{11} \) is an irrational number.

3. **Examine Option 3: \( \frac{2}{5} \)**
- This is already in the form \( \frac{p}{q} \) where \( p = 2 \) and \( q = 5 \).
- Hence, \( \frac{2}{5} \) is a rational number.

4. **Examine Option 4: \( \frac{3}{1} \)**
- This is also in the form \( \frac{p}{q} \) where \( p = 3 \) and \( q = 1 \).
- Thus, \( \frac{3}{1} \) is a rational number.

### Conclusion:
The only option that is an irrational number is **Option 2: \( \sqrt{11} \)**.