Simplify the radical expression.

−2–√+8–√−320−−√
(1 point)
Responses

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

−53–√
negative 5 square root of 3

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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To simplify the expression \(-2\sqrt{2} + 8\sqrt{3} - \sqrt{320}\), we first simplify \(\sqrt{320}\).

We can factor \(320\) as follows:

\[
320 = 64 \times 5 = 8^2 \times 5
\]

Therefore,

\[
\sqrt{320} = \sqrt{64 \times 5} = \sqrt{64} \cdot \sqrt{5} = 8\sqrt{5}
\]

Now substitute this back into the original expression:

\[
-2\sqrt{2} + 8\sqrt{3} - 8\sqrt{5}
\]

This expression is already simplified, and we can arrange it in a standard form:

\[
-2\sqrt{2} + 8\sqrt{3} - 8\sqrt{5}
\]

Now we match this with the provided responses:

- \(2\sqrt{2} - 6\sqrt{5}\)
- \(-5\sqrt{3}\)
- \(3\sqrt{2} - 6\sqrt{5}\)
- \(\sqrt{4} - 6\sqrt{5}\)

None of the responses match exactly, but let's break it down further.

If we rewrite \(-2\sqrt{2} + 8\sqrt{3} - 8\sqrt{5}\), we note there's no immediate match with your answer selections.

Hence, if we categorize and format, we have:

\(-2\sqrt{2} + 8\sqrt{3} - 8\sqrt{5}\).

But, this might represent a form of the \(8\sqrt{3} - 8\sqrt{5} - 2\sqrt{2}\) depending on how they expect the answer.

So, none of the choices are fitting straight directly as they are listed being that mixed in the format. You may need to check the values represented or clarified.

It looks like the closest resemblance would be around the structure presented weighing in and using combinations around if none fit. Clear to observe the end framed selected arrangements instead.