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

Answer 1

To simplify the expression \(-\sqrt{2} + \sqrt{8} - 3\sqrt{20}\), we start by simplifying the square roots involved.

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

2. Simplify \(\sqrt{20}\): \[ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} \] Therefore, \(3\sqrt{20} = 3 \cdot 2\sqrt{5} = 6\sqrt{5}\).

Now we can rewrite the original expression: \[ -\sqrt{2} + \sqrt{8} - 3\sqrt{20} = -\sqrt{2} + 2\sqrt{2} - 6\sqrt{5} \]

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

Thus, the entire expression simplifies to: \[ \sqrt{2} - 6\sqrt{5} \]

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

The answer is: \[ \sqrt{2} - 6\sqrt{5} \]