If `sqrt(7)=2.646`, then the value of `(1)/(sqrt(28))` up to three places of decimal is

Options

A. `0.183`
B. `0.185`
C. `0.187`
D. `0.189`

Answer

To find the value of \( \frac{1}{\sqrt{28}} \) using the given value \( \sqrt{7} = 2.646 \), we can follow these steps:

### Step 1: Simplify \( \sqrt{28} \)

We can express \( \sqrt{28} \) in terms of \( \sqrt{7} \):
\[ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2 \times \sqrt{7} \]

### Step 2: Substitute the value of \( \sqrt{7} \)

Now, we substitute the given value of \( \sqrt{7} \):
\[ \sqrt{28} = 2 \times 2.646 = 5.292 \]

### Step 3: Calculate \( \frac{1}{\sqrt{28}} \)

Now we can find \( \frac{1}{\sqrt{28}} \):
\[ \frac{1}{\sqrt{28}} = \frac{1}{5.292} \]

### Step 4: Perform the division

Now we perform the division to find the value:
\[ \frac{1}{5.292} \approx 0.189 \]

### Step 5: Round to three decimal places

Finally, we round the result to three decimal places:
\[ 0.189 \]

Thus, the value of \( \frac{1}{\sqrt{28}} \) up to three decimal places is \( 0.189 \).