The problem asks us to simplify the expression $\sqrt{12} + \sqrt{75} - 3\sqrt{27}$.

1. Problem Description

The problem asks us to simplify the expression $\sqrt{12} + \sqrt{75} - 3\sqrt{27}$.

2. Solution Steps

First, simplify each square root term:

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

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

$\sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}$

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

$2\sqrt{3} + 5\sqrt{3} - 3(3\sqrt{3}) = 2\sqrt{3} + 5\sqrt{3} - 9\sqrt{3}$

Combine the terms:

$(2 + 5 - 9)\sqrt{3} = (7 - 9)\sqrt{3} = -2\sqrt{3}$

3. Final Answer

The simplified expression is $-2\sqrt{3}$.