Mean proportional between 17 and 68 is

Options

A. 51
B. 24
C. 4
D. 34

Answer

To find the mean proportional between 17 and 68, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mean Proportional**:
The mean proportional \( x \) between two numbers \( a \) and \( b \) can be defined using the ratio:
\[ \frac{a}{x} = \frac{x}{b} \]
Here, \( a = 17 \) and \( b = 68 \).

2. **Setting up the Equation**:
We can set up the equation based on the definition:
\[ \frac{17}{x} = \frac{x}{68} \]

3. **Cross Multiplying**:
Cross-multiply to eliminate the fractions:
\[ 17 \cdot 68 = x \cdot x \]
This simplifies to:
\[ 1156 = x^2 \]

4. **Solving for \( x \)**:
To find \( x \), take the square root of both sides:
\[ x = \sqrt{1156} \]

5. **Calculating the Square Root**:
Now, calculate the square root:
\[ x = 34 \]

6. **Conclusion**:
Therefore, the mean proportional between 17 and 68 is:
\[ \boxed{34} \]