What will be the mean proportional between 4 and 25?

Answer

To find the mean proportional between 4 and 25, we can follow these steps:

### Step 1: Understand the concept of mean proportional
The mean proportional \( B \) between two numbers \( A \) and \( C \) is defined by the relationship:
\[ \frac{A}{B} = \frac{B}{C} \]
This means that \( B^2 = A \times C \).

### Step 2: Assign values to A and C
In this case, we have:
- \( A = 4 \)
- \( C = 25 \)

### Step 3: Set up the equation
Using the formula for mean proportional:
\[ B^2 = A \times C \]
Substituting the values of \( A \) and \( C \):
\[ B^2 = 4 \times 25 \]

### Step 4: Calculate \( A \times C \)
Now, calculate \( 4 \times 25 \):
\[ 4 \times 25 = 100 \]
So, we have:
\[ B^2 = 100 \]

### Step 5: Solve for \( B \)
To find \( B \), take the square root of both sides:
\[ B = \sqrt{100} \]
Calculating the square root gives:
\[ B = 10 \]

### Final Answer
The mean proportional between 4 and 25 is \( B = 10 \).

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