6) 2sqrt [4](48)-2sqrt (3)-sqrt [4](3)

To simplify \(2\sqrt[4]{48} - 2\sqrt{3} - \sqrt[4]{3}\), we need to break down each term and see if there are any common factors or simplifications possible.<br /><br />First, let's rewrite \(2\sqrt[4]{48}\):<br />\[ 2\sqrt[4]{48} = 2 \cdot \sqrt[4]{16 \cdot 3} = 2 \cdot \sqrt[4]{16} \cdot \sqrt[4]{3} = 2 \cdot 2 \cdot \sqrt[4]{3} = 4\sqrt[4]{3} \]<br /><br />So the expression becomes:<br />\[ 4\sqrt[4]{3} - 2\sqrt{3} - \sqrt[4]{3} \]<br /><br />Next, combine the \(\sqrt[4]{3}\) terms:<br />\[ 4\sqrt[4]{3} - \sqrt[4]{3} = (4 - 1)\sqrt[4]{3} = 3\sqrt[4]{3} \]<br /><br />Now the expression is:<br />\[ 3\sqrt[4]{3} - 2\sqrt{3} \]<br /><br />Since there are no further simplifications possible between the terms \(\sqrt[4]{3}\) and \(\sqrt{3}\), the final simplified form of the expression is:<br />\[ 3\sqrt[4]{3} - 2\sqrt{3} \]<br /><br />Thus, the simplified expression is:<br />\[ \boxed{3\sqrt[4]{3} - 2\sqrt{3}} \]