Simplify the expression $\sqrt{75} - \sqrt{192}$.

1. Problem Description

Simplify the expression $\sqrt{75} - \sqrt{192}$.

2. Solution Steps

We simplify each term separately.

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

$\sqrt{192} = \sqrt{64 \cdot 3} = \sqrt{64} \cdot \sqrt{3} = 8\sqrt{3}$

Then, we substitute the simplified terms back into the expression:

$\sqrt{75} - \sqrt{192} = 5\sqrt{3} - 8\sqrt{3} = (5-8)\sqrt{3} = -3\sqrt{3}$

3. Final Answer

$-3\sqrt{3}$