If `sqrt(15)=3.88` , the value of `sqrt(5/3)` is

Options

A. `1.29bar3`
B. 1.2934
C. 1.29
D. 1.295

Answer

To find the value of \(\sqrt{\frac{5}{3}}\) given that \(\sqrt{15} = 3.88\), we can follow these steps:

### Step 1: Rewrite \(\sqrt{\frac{5}{3}}\)
We can express \(\sqrt{\frac{5}{3}}\) in a different form:
\[ \sqrt{\frac{5}{3}} = \frac{\sqrt{5}}{\sqrt{3}} \]

### Step 2: Relate \(\sqrt{5}\) and \(\sqrt{15}\)
We know that:
\[ \sqrt{15} = \sqrt{5 \cdot 3} = \sqrt{5} \cdot \sqrt{3} \]
Thus, we can express \(\sqrt{5}\) in terms of \(\sqrt{15}\) and \(\sqrt{3}\):
\[ \sqrt{5} = \frac{\sqrt{15}}{\sqrt{3}} \]

### Step 3: Substitute \(\sqrt{15}\) into the equation
Now we can substitute \(\sqrt{15}\) into our expression for \(\sqrt{5}\):
\[ \sqrt{5} = \frac{3.88}{\sqrt{3}} \]

### Step 4: Substitute back into \(\sqrt{\frac{5}{3}}\)
Now we can substitute \(\sqrt{5}\) back into our expression for \(\sqrt{\frac{5}{3}}\):
\[ \sqrt{\frac{5}{3}} = \frac{\sqrt{5}}{\sqrt{3}} = \frac{\frac{3.88}{\sqrt{3}}}{\sqrt{3}} = \frac{3.88}{3} \]

### Step 5: Calculate \(\frac{3.88}{3}\)
Now we perform the division:
\[ \frac{3.88}{3} \approx 1.2933 \]

### Final Result
Thus, the value of \(\sqrt{\frac{5}{3}}\) is approximately:
\[ \sqrt{\frac{5}{3}} \approx 1.2933 \]