Simplify the radical expression.

−2–√+8–√−320−−√
(1 point)
Responses

2–√−65–√
square root of 2 minus 6 square root of 5

32–√−65–√
3 square root of 2 minus 6 square root of 5

4–√−65–√
square root of 4 minus 6 square root of 5

−53–√

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To simplify the expression \(-2\sqrt{2} + 8\sqrt{8} - \sqrt{320}\), we will first simplify each of the radical terms.

1. **Simplifying \(8\sqrt{8}\):**
\[
8\sqrt{8} = 8\sqrt{4 \cdot 2} = 8\cdot\sqrt{4}\cdot\sqrt{2} = 8 \cdot 2 \cdot \sqrt{2} = 16\sqrt{2}
\]

2. **Simplifying \(\sqrt{320}\):**
\[
\sqrt{320} = \sqrt{64 \cdot 5} = \sqrt{64}\cdot\sqrt{5} = 8\sqrt{5}
\]

Now, substituting these simplifications back into the original expression:

\[
-2\sqrt{2} + 16\sqrt{2} - 8\sqrt{5}
\]

Next, we can combine the like terms:

\[
(-2\sqrt{2} + 16\sqrt{2}) - 8\sqrt{5} = (16 - 2)\sqrt{2} - 8\sqrt{5} = 14\sqrt{2} - 8\sqrt{5}
\]

Thus, the simplified expression is:

**\(14\sqrt{2} - 8\sqrt{5}\)**

However, this does not match any of the provided responses. It seems you provided responses with different formats of square roots, and none match my result.

If you need the terms factored or further simplified, please clarify, but the direct simplification leads to \(14\sqrt{2} - 8\sqrt{5}\).