Find the mean proportional between 9 and 64.

Options

A. 25
B. 24
C. 27
D. 35

Answer

To find the mean proportional between 9 and 64, 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 can be rearranged to:
\[ B^2 = A \times C \]

### Step 2: Identify the values of \( A \) and \( C \)
In this problem, we have:
- \( A = 9 \)
- \( C = 64 \)

### Step 3: Substitute the values into the equation
Using the formula from Step 1:
\[ B^2 = 9 \times 64 \]

### Step 4: Calculate the product
Now, we calculate \( 9 \times 64 \):
\[ 9 \times 64 = 576 \]

### Step 5: Solve for \( B \)
Now, we take the square root of both sides to find \( B \):
\[ B = \sqrt{576} \]

### Step 6: Calculate the square root
Calculating the square root:
\[ B = 24 \]

### Conclusion
Thus, the mean proportional between 9 and 64 is \( 24 \).

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