State, with reason which of the are surds and which are not :
`root(3)(-125)`

Answer

To determine whether the expression \( \sqrt[3]{-125} \) is a surd or not, we will follow these steps:

### Step 1: Understand what a surd is
A surd is defined as an irrational number that can be expressed in the form of a root (like square roots, cube roots, etc.) but cannot be simplified to a rational number. Surds typically involve roots of positive integers.

### Step 2: Analyze the given expression
The expression given is \( \sqrt[3]{-125} \). This is a cube root of a negative number.

### Step 3: Calculate the cube root
The cube root of \(-125\) can be calculated as follows:
\[ \sqrt[3]{-125} = -5 \]
This is because \((-5) \times (-5) \times (-5) = -125\).

### Step 4: Determine if the result is rational or irrational
The result of the cube root, which is \(-5\), is a rational number since it can be expressed as a fraction \(-5/1\).

### Step 5: Conclusion
Since the result of \( \sqrt[3]{-125} \) is a rational number, it is not a surd.

### Final Answer
- **Surds**: None
- **Not Surds**: \( \sqrt[3]{-125} \) (because it equals \(-5\), which is rational)