Geometric mean of 4 and 9 is ________.

Answer

To find the geometric mean of the numbers 4 and 9, 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:
\[ GM = \sqrt{a \cdot b} \]

### Step 2: Identify the numbers
In this case, we have:
- \( a = 4 \)
- \( b = 9 \)

### Step 3: Substitute the values into the formula
Now, we substitute the values of \( a \) and \( b \) into the formula:
\[ GM = \sqrt{4 \cdot 9} \]

### Step 4: Calculate the product
Next, we calculate the product of 4 and 9:
\[ 4 \cdot 9 = 36 \]

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

### Step 6: Simplify the square root
The square root of 36 is:
\[ \sqrt{36} = 6 \]

### Final Answer
Thus, the geometric mean of 4 and 9 is:
\[ \text{Geometric Mean} = 6 \]

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