`sqrt (((0 cdot 324)/(10))` =?

Options

A. 0.18
B. `0 cdot 1`
C. `cdot 0018`
D. `2 cdot 8`

Answer

To solve the problem \(\sqrt{\frac{0.324}{10}}\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt{\frac{0.324}{10}} \]
This can be rewritten as:
\[ \sqrt{\frac{0.324}{10}} = \sqrt{\frac{324}{1000}} \]

### Step 2: Simplify the fraction
Next, we can express \(0.324\) as \(\frac{324}{1000}\) since \(0.324\) is equivalent to \(\frac{324}{1000}\). Thus, we have:
\[ \sqrt{\frac{324}{1000}} = \sqrt{\frac{324}{10^3}} = \sqrt{\frac{324}{10^2 \cdot 10}} = \sqrt{\frac{324}{100} \cdot \frac{1}{10}} = \sqrt{\frac{324}{100}} \cdot \sqrt{\frac{1}{10}} \]

### Step 3: Calculate the square roots
Now we can calculate the square roots separately:
\[ \sqrt{\frac{324}{100}} = \frac{\sqrt{324}}{\sqrt{100}} = \frac{18}{10} = 1.8 \]
And:
\[ \sqrt{\frac{1}{10}} = \frac{1}{\sqrt{10}} \approx 0.316 \]

### Step 4: Combine the results
Now we combine the results:
\[ \sqrt{\frac{324}{1000}} = 1.8 \cdot \frac{1}{\sqrt{10}} \approx 1.8 \cdot 0.316 \approx 0.18 \]

### Final Answer
Thus, the final answer is:
\[ \sqrt{\frac{0.324}{10}} = 0.18 \]