To simplify the expression \(6\sqrt{104} - \sqrt{26}\), we can start by simplifying \(\sqrt{104}\).
First, we factor \(104\): \[ 104 = 4 \times 26 \]
Now, we can simplify \(\sqrt{104}\): \[ \sqrt{104} = \sqrt{4 \times 26} = \sqrt{4} \times \sqrt{26} = 2\sqrt{26} \]
Now, we substitute \(\sqrt{104}\) back into the original expression: \[ 6\sqrt{104} - \sqrt{26} = 6(2\sqrt{26}) - \sqrt{26} \] \[ = 12\sqrt{26} - \sqrt{26} \]
Now, combine the terms: \[ 12\sqrt{26} - \sqrt{26} = (12 - 1)\sqrt{26} = 11\sqrt{26} \]
Thus, the simplified expression is: \[ \boxed{11\sqrt{26}} \]