State, with reason which of the are surds and which are not :
`sqrt(3+sqrt(2))`

Answer

To determine whether the expression \( \sqrt{3 + \sqrt{2}} \) is a surd or not, we will analyze it step by step.

### Step-by-Step Solution:

1. **Identify the Inner Expression**:
We start with the expression inside the square root: \( 3 + \sqrt{2} \).

2. **Evaluate \( \sqrt{2} \)**:
The number \( \sqrt{2} \) is known to be an irrational number. This is because it cannot be expressed as a fraction of two integers.

3. **Add 3 to \( \sqrt{2} \)**:
When we add 3 (which is a rational number) to \( \sqrt{2} \), the result \( 3 + \sqrt{2} \) remains irrational. This is because the sum of a rational number and an irrational number is always irrational.

4. **Take the Square Root**:
Now we take the square root of the entire expression: \( \sqrt{3 + \sqrt{2}} \). Since \( 3 + \sqrt{2} \) is irrational, the square root of an irrational number is also irrational.

5. **Determine if it is a Surd**:
A surd is defined as an expression containing a root that cannot be simplified to remove the root. Since \( \sqrt{3 + \sqrt{2}} \) cannot be simplified to a rational number or a perfect square, it is indeed a surd.

### Conclusion:
Thus, \( \sqrt{3 + \sqrt{2}} \) is a surd because it contains a square root that cannot be simplified to yield a rational number.