Find the G.M. of 4,12,36 , which are in G.P.

Answer

To find the geometric mean (G.M.) of the numbers 4, 12, and 36, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Geometric Mean**: The geometric mean of \( n \) numbers is given by the formula:
\[ G.M. = \sqrt[n]{x_1 \times x_2 \times \ldots \times x_n} \]
where \( x_1, x_2, \ldots, x_n \) are the numbers.

2. **Identify the Numbers**: Here, we have three numbers: 4, 12, and 36.

3. **Calculate the Product**: First, we need to multiply these three numbers together:
\[ 4 \times 12 \times 36 \]

4. **Perform the Multiplication**:
- First, multiply 4 and 12:
\[ 4 \times 12 = 48 \]
- Next, multiply the result by 36:
\[ 48 \times 36 \]
- To calculate \( 48 \times 36 \):
\[ 48 \times 36 = 1728 \]

5. **Take the Cube Root**: Now, we need to find the cube root of the product:
\[ G.M. = \sqrt[3]{1728} \]

6. **Calculate the Cube Root**: The cube root of 1728 is:
\[ \sqrt[3]{1728} = 12 \]

7. **Conclusion**: Therefore, the geometric mean of the numbers 4, 12, and 36 is:
\[ G.M. = 12 \]