`sqrt (0.1)` =?

Options

A. `0.1`
B. `0.01`
C. `0.316`
D. none of these

Answer

To solve the question \( \sqrt{0.1} \), we can follow these steps:

### Step 1: Rewrite the number in a simpler form
We can express \( 0.1 \) as a fraction:
\[ 0.1 = \frac{1}{10} \]

### Step 2: Apply the square root to the fraction
Using the property of square roots that states \( \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \), we can rewrite the square root of \( 0.1 \):
\[ \sqrt{0.1} = \sqrt{\frac{1}{10}} = \frac{\sqrt{1}}{\sqrt{10}} \]

### Step 3: Simplify the square root
Since \( \sqrt{1} = 1 \), we have:
\[ \sqrt{0.1} = \frac{1}{\sqrt{10}} \]

### Step 4: Calculate \( \sqrt{10} \)
The approximate value of \( \sqrt{10} \) is about \( 3.16 \). Therefore, we can substitute this value into our equation:
\[ \sqrt{0.1} \approx \frac{1}{3.16} \]

### Step 5: Perform the division
Now, we can calculate \( \frac{1}{3.16} \):
\[ \frac{1}{3.16} \approx 0.316 \]

### Final Answer
Thus, the value of \( \sqrt{0.1} \) is approximately:
\[ \sqrt{0.1} \approx 0.316 \]