Find the mean proportion between :
3 . 6, 1.8

Answer

To find the mean proportion between 3.6 and 1.8, we can follow these steps:

### Step 1: Set up the equation
Let \( X \) be the mean proportion. According to the definition of mean proportion, we can express it as:
\[ \frac{3.6}{X} = \frac{X}{1.8} \]

### Step 2: Cross-multiply
Cross-multiplying gives us:
\[ 3.6 \cdot 1.8 = X \cdot X \]
or
\[ 3.6 \cdot 1.8 = X^2 \]

### Step 3: Calculate the product of the extremes
Now, we need to calculate \( 3.6 \cdot 1.8 \):
\[ 3.6 \cdot 1.8 = 6.48 \]

### Step 4: Set up the equation for \( X \)
Now we have:
\[ X^2 = 6.48 \]

### Step 5: Solve for \( X \)
To find \( X \), we take the square root of both sides:
\[ X = \sqrt{6.48} \]

### Step 6: Calculate the square root
Calculating the square root:
\[ X \approx 2.54 \]

### Final Answer
Thus, the mean proportion between 3.6 and 1.8 is approximately \( 2.54 \).

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