Question
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–√
Answers
GPT-4o mini
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:
\[
\boxed{-4\sqrt{2} - 8\sqrt{5}}
\]
However, the provided responses did not list this expression. If your question meant combining or rearranging terms differently, please clarify which option you're considering, and I can further assist you!
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:
\[
\boxed{-4\sqrt{2} - 8\sqrt{5}}
\]
However, the provided responses did not list this expression. If your question meant combining or rearranging terms differently, please clarify which option you're considering, and I can further assist you!