By how much does `sqrt(12)+sqrt(18)` exceed `sqrt(3)+sqrt(2)` ?

Options

A. `2(sqrt(3)-sqrt(2))`
B. `2(sqrt(3)+sqrt(2))`
C. `sqrt(3)+2sqrt(2)`
D. `sqrt(2)-4sqrt(3)`

Answer

To solve the question "By how much does `sqrt(12) + sqrt(18)` exceed `sqrt(3) + sqrt(2)`?", we will follow these steps:

### Step 1: Simplify `sqrt(12)` and `sqrt(18)`
We can simplify the square roots:
- `sqrt(12) = sqrt(4 * 3) = sqrt(4) * sqrt(3) = 2 * sqrt(3)`
- `sqrt(18) = sqrt(9 * 2) = sqrt(9) * sqrt(2) = 3 * sqrt(2)`

### Step 2: Combine the simplified square roots
Now we can combine the simplified forms:
- `sqrt(12) + sqrt(18) = 2 * sqrt(3) + 3 * sqrt(2)`

### Step 3: Simplify `sqrt(3) + sqrt(2)`
The expression `sqrt(3) + sqrt(2)` remains as it is since it cannot be simplified further.

### Step 4: Find the difference
Now we need to find how much `sqrt(12) + sqrt(18)` exceeds `sqrt(3) + sqrt(2)`:
- Difference = `(2 * sqrt(3) + 3 * sqrt(2)) - (sqrt(3) + sqrt(2))`

### Step 5: Combine like terms
Now, we combine the like terms:
- Difference = `(2 * sqrt(3) - sqrt(3)) + (3 * sqrt(2) - sqrt(2))`
- Difference = `1 * sqrt(3) + 2 * sqrt(2)`

### Final Answer
Thus, `sqrt(12) + sqrt(18)` exceeds `sqrt(3) + sqrt(2)` by `sqrt(3) + 2 * sqrt(2)`.