If `sqrt(33)=5.745`, then the value of `sqrt((3)/(11)` is approximately

Options

A. A) `1`
B. B) `0.5223`
C. C) `6.32`
D. D) `2.035`

Answer

To find the value of \(\sqrt{\frac{3}{11}}\) using the given information that \(\sqrt{33} = 5.745\), we can follow these steps:

### Step 1: Rewrite the Expression
We start with the expression \(\sqrt{\frac{3}{11}}\). We can rewrite this expression as:
\[ \sqrt{\frac{3}{11}} = \frac{\sqrt{3}}{\sqrt{11}} \]

### Step 2: Relate to \(\sqrt{33}\)
Next, we can relate \(\sqrt{3}\) and \(\sqrt{11}\) to \(\sqrt{33}\). We know that:
\[ 33 = 3 \times 11 \]
Thus, we can express \(\sqrt{33}\) as:
\[ \sqrt{33} = \sqrt{3 \times 11} = \sqrt{3} \times \sqrt{11} \]

### Step 3: Express \(\sqrt{3}\) in terms of \(\sqrt{33}\)
From the previous step, we can express \(\sqrt{3}\) as:
\[ \sqrt{3} = \frac{\sqrt{33}}{\sqrt{11}} \]
Substituting this back into our expression for \(\sqrt{\frac{3}{11}}\):
\[ \sqrt{\frac{3}{11}} = \frac{\sqrt{3}}{\sqrt{11}} = \frac{\frac{\sqrt{33}}{\sqrt{11}}}{\sqrt{11}} = \frac{\sqrt{33}}{11} \]

### Step 4: Substitute the Value of \(\sqrt{33}\)
Now, we substitute the value of \(\sqrt{33}\) into the expression:
\[ \sqrt{\frac{3}{11}} = \frac{5.745}{11} \]

### Step 5: Calculate the Final Value
Now, we perform the division:
\[ \frac{5.745}{11} \approx 0.5223 \]

### Conclusion
Thus, the approximate value of \(\sqrt{\frac{3}{11}}\) is:
\[ \sqrt{\frac{3}{11}} \approx 0.5223 \]