Find the geometric mean of 12 and 27.

Explanation

To find the geometric mean of the numbers 12 and 27, we can follow these steps:

### Step 1: Understand the formula for geometric mean
The geometric mean (GM) of two numbers A and B is given by the formula:
\[ GM = \sqrt{A \times B} \]

### Step 2: Identify the values of A and B
In this case, we have:
- \( A = 12 \)
- \( B = 27 \)

### Step 3: Substitute the values into the formula
Now, we substitute the values of A and B into the formula:
\[ GM = \sqrt{12 \times 27} \]

### Step 4: Calculate the product of A and B
Next, we calculate the product:
\[ 12 \times 27 = 324 \]

### Step 5: Calculate the square root
Now, we find the square root of 324:
\[ GM = \sqrt{324} \]

### Step 6: Simplify the square root
The square root of 324 is:
\[ \sqrt{324} = 18 \]

### Conclusion
Thus, the geometric mean of 12 and 27 is:
\[ \boxed{18} \]

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