`sqrt2+ sqrt3+sqrt4+sqrt6` is equal to

Options

A. `cot (7 (1)/(2))^(@)`
B. `si (7 (1)/(2))^(@)`
C. `sin 15^(@)`
D. `cos 15^(@)`

Answer

To solve the expression \( \sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6} \), we can simplify it step by step.

### Step 1: Simplify the square roots
First, we notice that \( \sqrt{4} = 2 \). So we can rewrite the expression as:
\[ \sqrt{2} + \sqrt{3} + 2 + \sqrt{6} \]

### Step 2: Combine the constants
Now we can combine the constant term:
\[ 2 + \sqrt{2} + \sqrt{3} + \sqrt{6} \]

### Step 3: Approximate the square roots
Next, we can approximate the square roots to get a numerical value:
- \( \sqrt{2} \approx 1.414 \)
- \( \sqrt{3} \approx 1.732 \)
- \( \sqrt{6} \approx 2.449 \)

Now substituting these approximations into the expression:
\[ 2 + 1.414 + 1.732 + 2.449 \]

### Step 4: Perform the addition
Adding these values together:
\[ 2 + 1.414 = 3.414 \]
\[ 3.414 + 1.732 = 5.146 \]
\[ 5.146 + 2.449 \approx 7.595 \]

### Step 5: Final Result
Thus, the approximate value of \( \sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6} \) is approximately \( 7.595 \).

### Conclusion
The value of \( \sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6} \) is approximately \( 7.595 \).