Simplify the radical expression. −2–√+8–√−320−−√−2+8−320 (1 point) Responses 2–√−65–√2−65square root of 2 minus 6 square root of 5 −53–√−53negative 5 square root of 3 32–√−65–√32−653 square root of 2 minus 6 square root of 5 4–√−65–√

Answer 1

To simplify the expression \(-2\sqrt{8} - \sqrt{320}\):

1. First, simplify \(\sqrt{8}\): \[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \] Therefore, \[ -2\sqrt{8} = -2(2\sqrt{2}) = -4\sqrt{2} \]

2. Next, simplify \(\sqrt{320}\): \[ \sqrt{320} = \sqrt{64 \times 5} = \sqrt{64} \cdot \sqrt{5} = 8\sqrt{5} \]

3. Now substitute these simplified forms back into the expression: \[ -4\sqrt{2} - 8\sqrt{5} \]

Thus, the simplified form of the expression \(-2\sqrt{8} - \sqrt{320}\) is: \[ \boxed{-4\sqrt{2} - 8\sqrt{5}} \]

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