The mean proportional between 2 and 32 is.

Answer

To find the mean proportional between the numbers 2 and 32, we can follow these steps:

### Step 1: Understand the concept of mean proportional
The mean proportional \( x \) between two numbers \( A \) and \( B \) can be defined using the ratio:
\[ \frac{A}{x} = \frac{x}{B} \]
This means that \( A \) is to \( x \) as \( x \) is to \( B \).

### Step 2: Set up the equation
Given \( A = 2 \) and \( B = 32 \), we can set up the equation:
\[ \frac{2}{x} = \frac{x}{32} \]

### Step 3: Cross-multiply
Cross-multiplying gives us:
\[ 2 \cdot 32 = x \cdot x \]
This simplifies to:
\[ 64 = x^2 \]

### Step 4: Solve for \( x \)
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{64} \]
Calculating the square root gives:
\[ x = 8 \]

### Conclusion
Thus, the mean proportional between 2 and 32 is:
\[ \boxed{8} \]

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