The mean proportional of `0cdot32` and `0cdot02` is-

Options

A. `0cdot08`
B. `0cdot16`
C. `0cdot30`
D. `0cdot34`

Answer

To find the mean proportional of the numbers \(0.32\) and \(0.02\), we can use the formula for the mean proportional between two numbers \(A\) and \(B\):

\[ \text{Mean Proportional} = \sqrt{A \times B} \]

### Step-by-Step Solution:

1. **Identify the Numbers**:
Let \(A = 0.32\) and \(B = 0.02\).

2. **Multiply the Numbers**:
Calculate the product of \(A\) and \(B\):
\[ A \times B = 0.32 \times 0.02 \]

3. **Convert to Fraction**:
To simplify the multiplication, convert the decimals to fractions:
\[ 0.32 = \frac{32}{100} \quad \text{and} \quad 0.02 = \frac{2}{100} \]
Thus,
\[ A \times B = \frac{32}{100} \times \frac{2}{100} = \frac{64}{10000} \]

4. **Take the Square Root**:
Now, take the square root of the product:
\[ \sqrt{A \times B} = \sqrt{\frac{64}{10000}} = \frac{\sqrt{64}}{\sqrt{10000}} = \frac{8}{100} \]

5. **Convert Back to Decimal**:
Convert \(\frac{8}{100}\) back to decimal form:
\[ \frac{8}{100} = 0.08 \]

### Final Answer:
The mean proportional of \(0.32\) and \(0.02\) is \(0.08\).

---