`root3(ab)= (root3(a)) xx (..........)`

Options

A. `root 3(a)`
B. `root 2(a)`
C. `1/root 3(b)`
D. `root 3(b)`

Answer

To solve the question \( \sqrt[3]{ab} = \sqrt[3]{a} \times \text{(..........)} \), we will use the properties of cube roots.

### Step-by-Step Solution:

1. **Understanding the Cube Root**: The cube root of a product can be expressed in terms of the cube roots of the individual factors. This is a property of cube roots.

2. **Applying the Property**: According to the property of cube roots, we can write:
\[ \sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b} \]

3. **Filling in the Blank**: From the above equation, we can see that:
\[ \sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b} \]
Therefore, the blank can be filled with \( \sqrt[3]{b} \).

4. **Final Answer**: Thus, we conclude that:
\[ \sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b} \]

### Summary:
The complete equation is:
\[ \sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b} \]