Find the mean proportional between 8 and 18.

Answer

To find the mean proportional between two numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Mean Proportional**:
Let the mean proportional between 8 and 18 be denoted as \( x \).

2. **Set Up the Equation**:
The mean proportional is defined such that:
\[ \frac{8}{x} = \frac{x}{18} \]
This means that \( x \) is the mean proportional between 8 and 18.

3. **Cross Multiply**:
To eliminate the fractions, we can cross-multiply:
\[ 8 \cdot 18 = x \cdot x \]
This simplifies to:
\[ 144 = x^2 \]

4. **Solve for \( x \)**:
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{144} \]

5. **Calculate the Square Root**:
The square root of 144 is:
\[ x = 12 \]

6. **Conclusion**:
Therefore, the mean proportional between 8 and 18 is:
\[ \boxed{12} \]