If `sqrt(6) =2.55`, then the value of `sqrt(2/3) + sqrt(3/2)` is:

Options

A. 4.48
B. 4.49
C. 4.5
D. 2.06

Answer

To solve the expression \( \sqrt{\frac{2}{3}} + \sqrt{\frac{3}{2}} \) given that \( \sqrt{6} = 2.55 \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt{\frac{2}{3}} + \sqrt{\frac{3}{2}} \]

### Step 2: Find a common denominator
To add these two fractions, we need a common denominator. We can express both terms with a common denominator of \( \sqrt{6} \):
\[ \sqrt{\frac{2}{3}} = \frac{\sqrt{2}}{\sqrt{3}} \quad \text{and} \quad \sqrt{\frac{3}{2}} = \frac{\sqrt{3}}{\sqrt{2}} \]

### Step 3: Combine the fractions
Now, we can combine the two fractions:
\[ \frac{\sqrt{2}}{\sqrt{3}} + \frac{\sqrt{3}}{\sqrt{2}} = \frac{\sqrt{2} \cdot \sqrt{2} + \sqrt{3} \cdot \sqrt{3}}{\sqrt{2} \cdot \sqrt{3}} = \frac{2 + 3}{\sqrt{6}} = \frac{5}{\sqrt{6}} \]

### Step 4: Substitute the value of \( \sqrt{6} \)
Now, we substitute the value of \( \sqrt{6} \):
\[ \frac{5}{\sqrt{6}} = \frac{5}{2.55} \]

### Step 5: Calculate the final value
Now we perform the division:
\[ \frac{5}{2.55} \approx 1.96078 \]
Rounding this to two decimal places, we get:
\[ 1.96 \]

Thus, the value of \( \sqrt{\frac{2}{3}} + \sqrt{\frac{3}{2}} \) is approximately \( 1.96 \).

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