If the value of `sqrt(30)` is approximately 5.477, then what is the approximate value of `sqrt(5/6)` ?

Options

A. 0.853
B. 0.891
C. 0.913
D. 0.937

Answer

To find the approximate value of \(\sqrt{\frac{5}{6}}\) using the given value of \(\sqrt{30} \approx 5.477\), we can follow these steps:

### Step 1: Rewrite \(\sqrt{\frac{5}{6}}\)
We can express \(\sqrt{\frac{5}{6}}\) in a form that utilizes \(\sqrt{30}\). We can multiply and divide by 6:

\[ \sqrt{\frac{5}{6}} = \sqrt{\frac{5 \cdot 6}{6 \cdot 6}} = \sqrt{\frac{30}{36}} \]

### Step 2: Simplify the expression
Now we can separate the square root:

\[ \sqrt{\frac{30}{36}} = \frac{\sqrt{30}}{\sqrt{36}} \]

### Step 3: Calculate \(\sqrt{36}\)
We know that:

\[ \sqrt{36} = 6 \]

### Step 4: Substitute \(\sqrt{30}\)
Now we can substitute the approximate value of \(\sqrt{30}\):

\[ \sqrt{\frac{5}{6}} = \frac{\sqrt{30}}{6} \approx \frac{5.477}{6} \]

### Step 5: Perform the division
Now we perform the division:

\[ \frac{5.477}{6} \approx 0.913 \]

### Final Answer
Thus, the approximate value of \(\sqrt{\frac{5}{6}}\) is:

\[ \sqrt{\frac{5}{6}} \approx 0.913 \]