Question

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

Answer 1

To simplify the expression \(-2\sqrt{8} - \sqrt{320}\), let's break it down step by step.

1. **Simplifying \(-2\sqrt{8}\)**:
\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2 \sqrt{2}
\]
Thus,
\[
-2\sqrt{8} = -2 \cdot 2\sqrt{2} = -4\sqrt{2}
\]

2. **Simplifying \(-\sqrt{320}\)**:
\[
320 = 64 \cdot 5 \quad \text{(since } 64 = 8^2\text{)}
\]
Therefore,
\[
\sqrt{320} = \sqrt{64 \cdot 5} = \sqrt{64} \cdot \sqrt{5} = 8\sqrt{5}
\]
Thus,
\[
-\sqrt{320} = -8\sqrt{5}
\]

3. **Combining both parts**:
So we have:
\[
-4\sqrt{2} - 8\sqrt{5}
\]
This results in:
\[
-4\sqrt{2} - 8\sqrt{5}
\]

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

However, if we compare this with the provided response options, it seems none of the responses match this exactly. If you're looking for options that sound closest or contain common radicals or figures, please recheck or provide more context. Nonetheless, the simplified form of the expression is accurately calculated above.