The smallest of `sqrt(8)+sqrt(5)`, `sqrt(7)+sqrt(6)`, `sqrt(10)+sqrt(3)` and `sqrt(11)+sqrt(2)` is

Options

A. `sqrt(8)+sqrt(5)`
B. `sqrt(7)+sqrt(6)`
C. `sqrt(10)+sqrt(3)`
D. `sqrt(11)+sqrt(2)`

Answer

To find the smallest value among the expressions \( \sqrt{8} + \sqrt{5} \), \( \sqrt{7} + \sqrt{6} \), \( \sqrt{10} + \sqrt{3} \), and \( \sqrt{11} + \sqrt{2} \), we will evaluate each expression step by step.

### Step 1: Calculate \( \sqrt{8} + \sqrt{5} \)

First, we simplify \( \sqrt{8} \):
\[ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \]
Now we can approximate \( \sqrt{2} \approx 1.414 \):
\[ \sqrt{8} \approx 2 \times 1.414 = 2.828 \]
Next, we calculate \( \sqrt{5} \):
\[ \sqrt{5} \approx 2.236 \]
Now, we add these two results:
\[ \sqrt{8} + \sqrt{5} \approx 2.828 + 2.236 = 5.064 \]

### Step 2: Calculate \( \sqrt{7} + \sqrt{6} \)

Next, we approximate \( \sqrt{7} \) and \( \sqrt{6} \):
\[ \sqrt{7} \approx 2.646, \quad \sqrt{6} \approx 2.449 \]
Now we add these two results:
\[ \sqrt{7} + \sqrt{6} \approx 2.646 + 2.449 = 5.095 \]

### Step 3: Calculate \( \sqrt{10} + \sqrt{3} \)

Now we approximate \( \sqrt{10} \) and \( \sqrt{3} \):
\[ \sqrt{10} \approx 3.162, \quad \sqrt{3} \approx 1.732 \]
Now we add these two results:
\[ \sqrt{10} + \sqrt{3} \approx 3.162 + 1.732 = 4.894 \]

### Step 4: Calculate \( \sqrt{11} + \sqrt{2} \)

Finally, we approximate \( \sqrt{11} \) and \( \sqrt{2} \):
\[ \sqrt{11} \approx 3.317, \quad \sqrt{2} \approx 1.414 \]
Now we add these two results:
\[ \sqrt{11} + \sqrt{2} \approx 3.317 + 1.414 = 4.731 \]

### Step 5: Compare the results

Now we compare all the calculated sums:
- \( \sqrt{8} + \sqrt{5} \approx 5.064 \)
- \( \sqrt{7} + \sqrt{6} \approx 5.095 \)
- \( \sqrt{10} + \sqrt{3} \approx 4.894 \)
- \( \sqrt{11} + \sqrt{2} \approx 4.731 \)

The smallest value among these is:
\[ \sqrt{11} + \sqrt{2} \approx 4.731 \]

### Conclusion

Thus, the smallest of \( \sqrt{8} + \sqrt{5} \), \( \sqrt{7} + \sqrt{6} \), \( \sqrt{10} + \sqrt{3} \), and \( \sqrt{11} + \sqrt{2} \) is:
\[ \boxed{\sqrt{11} + \sqrt{2}} \]