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 calculate each expression step by step.

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

1. Find \( \sqrt{8} \):
\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \approx 2.83 \]

2. Find \( \sqrt{5} \):
\[ \sqrt{5} \approx 2.24 \]

3. Add the two results:
\[ \sqrt{8} + \sqrt{5} \approx 2.83 + 2.24 = 5.07 \]

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

1. Find \( \sqrt{7} \):
\[ \sqrt{7} \approx 2.65 \]

2. Find \( \sqrt{6} \):
\[ \sqrt{6} \approx 2.45 \]

3. Add the two results:
\[ \sqrt{7} + \sqrt{6} \approx 2.65 + 2.45 = 5.10 \]

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

1. Find \( \sqrt{10} \):
\[ \sqrt{10} \approx 3.16 \]

2. Find \( \sqrt{3} \):
\[ \sqrt{3} \approx 1.732 \]

3. Add the two results:
\[ \sqrt{10} + \sqrt{3} \approx 3.16 + 1.732 = 4.892 \approx 4.89 \]

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

1. Find \( \sqrt{11} \):
\[ \sqrt{11} \approx 3.32 \]

2. Find \( \sqrt{2} \):
\[ \sqrt{2} \approx 1.41 \]

3. Add the two results:
\[ \sqrt{11} + \sqrt{2} \approx 3.32 + 1.41 = 4.73 \]

### Step 5: Compare all the results

Now we have calculated:
- \( \sqrt{8} + \sqrt{5} \approx 5.07 \)
- \( \sqrt{7} + \sqrt{6} \approx 5.10 \)
- \( \sqrt{10} + \sqrt{3} \approx 4.89 \)
- \( \sqrt{11} + \sqrt{2} \approx 4.73 \)

The smallest value among these is \( \sqrt{11} + \sqrt{2} \approx 4.73 \).

### Final Answer

The smallest of \( \sqrt{8} + \sqrt{5}, \sqrt{7} + \sqrt{6}, \sqrt{10} + \sqrt{3} \), and \( \sqrt{11} + \sqrt{2} \) is \( \sqrt{11} + \sqrt{2} \).

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