Find the geometric mean between
3 and 12

Answer

To find the geometric mean between the numbers 3 and 12, we can follow these steps:

### Step 1: Understand the formula for geometric mean
The geometric mean (GM) between 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:
- \( a = 3 \)
- \( b = 12 \)

### Step 3: Substitute the values into the formula
Now, we can substitute the values of \( a \) and \( b \) into the formula:
\[ GM = \sqrt{3 \times 12} \]

### Step 4: Calculate the product inside the square root
Next, we calculate the product:
\[ 3 \times 12 = 36 \]

### Step 5: Take the square root of the product
Now, we find the square root of 36:
\[ GM = \sqrt{36} = 6 \]

### Final Answer
Thus, the geometric mean between 3 and 12 is:
\[ \text{GM} = 6 \]

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