Find the mean proportion between : 3 . 6 and 1 . 6

Answer

To find the mean proportion between 3.6 and 1.6, we can follow these steps:

### Step 1: Define the values
Let \( A = 3.6 \) and \( B = 1.6 \).

### Step 2: Use the formula for mean proportion
The mean proportion \( X \) between two numbers \( A \) and \( B \) can be calculated using the formula:
\[ \frac{A}{X} = \frac{X}{B} \]
This implies:
\[ X^2 = A \times B \]

### Step 3: Substitute the values of A and B
Now, substitute the values of \( A \) and \( B \):
\[ X^2 = 3.6 \times 1.6 \]

### Step 4: Calculate the product
To calculate \( 3.6 \times 1.6 \):
\[ 3.6 = \frac{36}{10} \quad \text{and} \quad 1.6 = \frac{16}{10} \]
So,
\[ 3.6 \times 1.6 = \left(\frac{36}{10}\right) \times \left(\frac{16}{10}\right) = \frac{36 \times 16}{100} \]

### Step 5: Calculate \( 36 \times 16 \)
Now, calculate \( 36 \times 16 \):
\[ 36 \times 16 = 576 \]
Thus,
\[ X^2 = \frac{576}{100} = 5.76 \]

### Step 6: Take the square root
Now, take the square root to find \( X \):
\[ X = \sqrt{5.76} \]

### Step 7: Simplify the square root
Calculating \( \sqrt{5.76} \):
\[ \sqrt{5.76} = 2.4 \]

### Conclusion
Therefore, the mean proportion between 3.6 and 1.6 is \( 2.4 \).

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