If the HCF of two numbers is 6 and LCM of the same two numbers is 54, then the square root of the product of these numbers is:

Options

A. 24
B. 18
C. 12
D. 16

Answer

To solve the problem, we need to find the square root of the product of two numbers given their HCF (Highest Common Factor) and LCM (Least Common Multiple).

### Step-by-Step Solution:

1. **Understand the relationship between HCF, LCM, and the product of two numbers:**
The relationship is given by the formula:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

2. **Substitute the given values into the formula:**
We know that:
- HCF = 6
- LCM = 54

Therefore, we can substitute these values into the formula:
\[ 6 \times 54 = \text{Product of the two numbers} \]

3. **Calculate the product:**
Now, we perform the multiplication:
\[ 6 \times 54 = 324 \]
So, the product of the two numbers is 324.

4. **Find the square root of the product:**
Next, we need to find the square root of 324:
\[ \sqrt{324} = 18 \]

5. **Conclusion:**
The square root of the product of the two numbers is 18.

### Final Answer:
The square root of the product of the two numbers is **18**.