Simplify. 8sqrt (3)-4sqrt (27)+sqrt (12) square

To simplify the expression \(8\sqrt{3} - 4\sqrt{27} + \sqrt{12}\), we need to break down the square roots into simpler forms.<br /><br />First, let's simplify each square root term individually:<br /><br />1. \(\sqrt{27}\):<br /> \[<br /> \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}<br /> \]<br /><br />2. \(\sqrt{12}\):<br /> \[<br /> \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}<br /> \]<br /><br />Now substitute these simplified forms back into the original expression:<br /><br />\[<br />8\sqrt{3} - 4\sqrt{27} + \sqrt{12} = 8\sqrt{3} - 4(3\sqrt{3}) + 2\sqrt{3}<br />\]<br /><br />Next, combine the like terms:<br /><br />\[<br />8\sqrt{3} - 12\sqrt{3} + 2\sqrt{3}<br />\]<br /><br />Combine the coefficients of \(\sqrt{3}\):<br /><br />\[<br />(8 - 12 + 2)\sqrt{3} = (-4 + 2)\sqrt{3} = -2\sqrt{3}<br />\]<br /><br />Thus, the simplified form of the expression is:<br /><br />\[<br />\boxed{-2\sqrt{3}}<br />\]