Question

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

Answer 1

To simplify the expression \( -2\sqrt{8} - \sqrt{320} \), we first simplify the square roots.

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

2. **Simplify \(-\sqrt{320}\)**:
\[
\sqrt{320} = \sqrt{64 \times 5} = \sqrt{64} \cdot \sqrt{5} = 8\sqrt{5}
\]
Therefore,
\[
-\sqrt{320} = -8\sqrt{5}
\]

Now, substitute the simplified terms back into the expression:

\[
-4\sqrt{2} - 8\sqrt{5}
\]

This expression cannot be simplified further because \( \sqrt{2} \) and \( \sqrt{5} \) are not like terms.

So the final simplified result is:
\[
-4\sqrt{2} - 8\sqrt{5}
\]

Now looking at the responses you provided, you can rewrite this expression if needed based on how the options are formatted, but it won't match any exact one without further context.

If the options were intended to be matched against this expression, it looks like none of the provided answers matches this one exactly.

Please double-check if there's any mistake or confusion in the response options or if they need to correspond with the simplification we derived.