The problem asks to simplify the expression $\sqrt{48} - \sqrt{75} + \sqrt{12}$ and find the correct answer among the provided options: $\sqrt{3}$, $2\sqrt{3}$, $-\sqrt{3}$, and $-2\sqrt{3}$.

1. Problem Description

The problem asks to simplify the expression $\sqrt{48} - \sqrt{75} + \sqrt{12}$ and find the correct answer among the provided options: $\sqrt{3}$, $2\sqrt{3}$, $-\sqrt{3}$, and $-2\sqrt{3}$.

2. Solution Steps

First, we simplify each square root term:

$\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$

$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$

$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$

Now we substitute these simplified terms back into the original expression:

$\sqrt{48} - \sqrt{75} + \sqrt{12} = 4\sqrt{3} - 5\sqrt{3} + 2\sqrt{3}$

Combine the terms:

$4\sqrt{3} - 5\sqrt{3} + 2\sqrt{3} = (4 - 5 + 2)\sqrt{3} = (6 - 5)\sqrt{3} = 1\sqrt{3} = \sqrt{3}$

3. Final Answer

$\sqrt{3}$