Question

6 squareroot 104 - squareroot 26

Answer 1

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:
\[
\boxed{11\sqrt{26}}
\]