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

Options

A. A) `1.29bar3`
B. B) `1.2934`
C. C) `1.29`
D. 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 terms of \(\sqrt{15}\):
\[ \sqrt{\frac{5}{3}} = \sqrt{\frac{5}{15} \cdot 5} = \sqrt{\frac{5}{15}} \cdot \sqrt{5} \]
This is because \(\frac{5}{3}\) can be rewritten as \(\frac{5}{15} \cdot 5\).

### Step 2: Simplify \(\sqrt{\frac{5}{15}}\)
We can simplify \(\sqrt{\frac{5}{15}}\):
\[ \sqrt{\frac{5}{15}} = \sqrt{\frac{1}{3}} \cdot \sqrt{5} \]
This is because \(\frac{5}{15} = \frac{1}{3}\).

### Step 3: Substitute \(\sqrt{15}\)
Now, we can express \(\sqrt{\frac{5}{3}}\) as:
\[ \sqrt{\frac{5}{3}} = \sqrt{5} \cdot \frac{\sqrt{15}}{3} \]
We know that \(\sqrt{15} = 3.88\), so we can substitute this value in.

### Step 4: Calculate \(\sqrt{5}\)
Now we need to calculate \(\sqrt{5}\):
\[ \sqrt{5} = \frac{\sqrt{15}}{\sqrt{3}} = \frac{3.88}{\sqrt{3}} \]
To find \(\sqrt{3}\), we can use the approximation \(\sqrt{3} \approx 1.732\).

### Step 5: Calculate \(\sqrt{5}\)
Now we can calculate \(\sqrt{5}\):
\[ \sqrt{5} \approx \frac{3.88}{1.732} \approx 2.24 \]

### Step 6: Substitute back to find \(\sqrt{\frac{5}{3}}\)
Now substituting back to find \(\sqrt{\frac{5}{3}}\):
\[ \sqrt{\frac{5}{3}} = \frac{2.24}{3} \approx 0.7467 \]

### Step 7: Final Calculation
To find the final value of \(\sqrt{\frac{5}{3}}\):
\[ \sqrt{\frac{5}{3}} \approx 1.293 \]

### Conclusion
Thus, the value of \(\sqrt{\frac{5}{3}}\) is approximately \(1.293\).

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