Simplify the radical expression - sqrt(2) + sqrt(8) - 3sqrt(20) ( 1 point) sqrt(2) - 6sqrt(5); 3sqrt(2) - 6sqrt(5); sqrt(4) - 6sqrt(5) O - 5sqrt(3)

Answer 1

To simplify the expression \(-\sqrt{2} + \sqrt{8} - 3\sqrt{20}\), we'll start by simplifying \(\sqrt{8}\) and \(\sqrt{20}\).

1. Simplify \(\sqrt{8}\): \[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \]

2. Simplify \(\sqrt{20}\): \[ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} \]

Now, substitute these values back into the expression:

\(-\sqrt{2} + \sqrt{8} - 3\sqrt{20} = -\sqrt{2} + 2\sqrt{2} - 3(2\sqrt{5})\)

This simplifies to: \[ -\sqrt{2} + 2\sqrt{2} - 6\sqrt{5} \]

3. Combine the \(\sqrt{2}\) terms: \[ (-1 + 2)\sqrt{2} - 6\sqrt{5} = 1\sqrt{2} - 6\sqrt{5} = \sqrt{2} - 6\sqrt{5} \]

Thus, the simplified expression is: \[ \sqrt{2} - 6\sqrt{5} \]

So the correct answer is: \(\sqrt{2} - 6\sqrt{5}\)