If the HCF of two numbers is 12 and LCM of the same two numbers is 48, then the square root of the product of these numbers is:

Options

A. 16
B. 24
C. 48
D. 12

Answer

To solve the problem, we will use the relationship between the Highest Common Factor (HCF), Lowest Common Multiple (LCM), and the product of two numbers.

### Step-by-step Solution:

1. **Understand the relationship**: The product of two numbers (let's call them A and B) can be expressed in terms of their HCF and LCM. The formula is:
\[ A \times B = \text{HCF}(A, B) \times \text{LCM}(A, B) \]

2. **Identify the given values**: From the question, we know:
- HCF = 12
- LCM = 48

3. **Substitute the values into the formula**:
\[ A \times B = 12 \times 48 \]

4. **Calculate the product**:
\[ A \times B = 12 \times 48 = 576 \]

5. **Find the square root of the product**:
\[ \sqrt{A \times B} = \sqrt{576} \]

6. **Calculate the square root**:
\[ \sqrt{576} = 24 \]

### Final Answer:
The square root of the product of the two numbers is **24**.