If the value of `sqrt(42)` is approximately 6.480, then what is the approximate value of `sqrt(6//7)`?

Options

A. `0.925`
B. `0.935`
C. `0.945`
D. `0.955`

Answer

To find the approximate value of \( \sqrt{\frac{6}{7}} \), we can use the given information about \( \sqrt{42} \). Here’s a step-by-step solution:

### Step 1: Express \( \sqrt{\frac{6}{7}} \)
We start with the expression:
\[ \sqrt{\frac{6}{7}} = \sqrt{6} \cdot \frac{1}{\sqrt{7}} \]

### Step 2: Rewrite \( \sqrt{6} \) in terms of \( \sqrt{42} \)
To relate \( \sqrt{6} \) and \( \sqrt{7} \) to \( \sqrt{42} \), we can multiply and divide by 7:
\[ \sqrt{\frac{6}{7}} = \sqrt{\frac{6 \cdot 7}{7 \cdot 7}} = \sqrt{\frac{42}{49}} = \frac{\sqrt{42}}{\sqrt{49}} \]

### Step 3: Simplify \( \sqrt{49} \)
Since \( \sqrt{49} = 7 \), we can substitute this back into our equation:
\[ \sqrt{\frac{6}{7}} = \frac{\sqrt{42}}{7} \]

### Step 4: Substitute the value of \( \sqrt{42} \)
We know from the problem statement that \( \sqrt{42} \approx 6.480 \):
\[ \sqrt{\frac{6}{7}} \approx \frac{6.480}{7} \]

### Step 5: Calculate \( \frac{6.480}{7} \)
Now, we perform the division:
\[ \frac{6.480}{7} \approx 0.9257142857 \]

### Step 6: Round to three decimal places
Rounding \( 0.9257142857 \) gives us approximately:
\[ \sqrt{\frac{6}{7}} \approx 0.926 \]

### Conclusion
Thus, the approximate value of \( \sqrt{\frac{6}{7}} \) is \( 0.925 \).