Simplify the following
`(sqrt(3)-sqrt(2))^(2)`

Answer

To simplify the expression \((\sqrt{3} - \sqrt{2})^2\), we can use the formula for the square of a binomial, which is given by:

\[ (a - b)^2 = a^2 - 2ab + b^2 \]

In our case, we can identify:
- \(a = \sqrt{3}\)
- \(b = \sqrt{2}\)

Now, we can apply the formula step by step:

### Step 1: Identify \(a\) and \(b\)
Let \(a = \sqrt{3}\) and \(b = \sqrt{2}\).

### Step 2: Apply the formula
Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), we can substitute \(a\) and \(b\):

\[ (\sqrt{3} - \sqrt{2})^2 = (\sqrt{3})^2 - 2(\sqrt{3})(\sqrt{2}) + (\sqrt{2})^2 \]

### Step 3: Calculate \(a^2\) and \(b^2\)
Now, we calculate each term:
- \((\sqrt{3})^2 = 3\)
- \((\sqrt{2})^2 = 2\)

### Step 4: Calculate \(2ab\)
Next, we calculate \(2ab\):
\[ 2(\sqrt{3})(\sqrt{2}) = 2\sqrt{6} \]

### Step 5: Substitute back into the equation
Now, we can substitute these values back into the equation:
\[ (\sqrt{3} - \sqrt{2})^2 = 3 - 2\sqrt{6} + 2 \]

### Step 6: Combine like terms
Now, combine the constant terms:
\[ 3 + 2 = 5 \]
So, we have:
\[ (\sqrt{3} - \sqrt{2})^2 = 5 - 2\sqrt{6} \]

### Final Answer
Thus, the simplified form of \((\sqrt{3} - \sqrt{2})^2\) is:
\[ \boxed{5 - 2\sqrt{6}} \]