Find the mean proportional between 100 and 625.

Options

A. 350
B. 225
C. 250
D. 275

Answer

To find the mean proportional between 100 and 625, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Mean Proportional:**
The mean proportional \( x \) between two numbers \( A \) and \( B \) is defined such that:
\[ \frac{A}{x} = \frac{x}{B} \]
This implies that:
\[ x^2 = A \times B \]

2. **Identify the Numbers:**
Here, \( A = 100 \) and \( B = 625 \).

3. **Calculate the Product of A and B:**
We need to multiply \( A \) and \( B \):
\[ A \times B = 100 \times 625 \]

4. **Calculate the Product:**
\[ 100 \times 625 = 62500 \]

5. **Take the Square Root:**
Now, we find the mean proportional \( x \) by taking the square root of the product:
\[ x = \sqrt{62500} \]

6. **Simplify the Square Root:**
We can simplify \( \sqrt{62500} \):
\[ \sqrt{62500} = \sqrt{(100 \times 625)} = \sqrt{100} \times \sqrt{625} = 10 \times 25 = 250 \]

7. **Conclusion:**
Therefore, the mean proportional between 100 and 625 is:
\[ \boxed{250} \]