Geometric mean of 3, 9 and 27, is

Options

A. 18
B. 6
C. 9
D. none of these

Answer

To find the geometric mean of the numbers 3, 9, and 27, we can follow these steps:

### Step 1: Identify the numbers
The numbers we are working with are:
- \( A_1 = 3 \)
- \( A_2 = 9 \)
- \( A_3 = 27 \)

### Step 2: Multiply the numbers
We need to multiply these three numbers together:
\[ A_1 \times A_2 \times A_3 = 3 \times 9 \times 27 \]

### Step 3: Calculate the product
Now, let's calculate the product:
\[ 3 \times 9 = 27 \]
\[ 27 \times 27 = 729 \]
Thus, the product of the numbers is:
\[ 3 \times 9 \times 27 = 729 \]

### Step 4: Take the cube root
The geometric mean is found by taking the cube root of the product we calculated:
\[ \text{Geometric Mean} = \sqrt[3]{729} \]

### Step 5: Calculate the cube root
Now, we need to find the cube root of 729. We know that:
\[ 9 \times 9 \times 9 = 729 \]
So, the cube root of 729 is:
\[ \sqrt[3]{729} = 9 \]

### Final Answer
The geometric mean of 3, 9, and 27 is:
\[ \boxed{9} \]

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