Which expression simplifies to 87–√3 ?(1 point) Responses −67–√3−27–√3 negative 6 cube root of 7 minus 2 cube root of 7 36–√3+51–√3 3 cube root of 6 plus 5 cube root of 1 256−−√3−47–√3 2 cube root of 56 minus 4 cube root of 7 56−−√3+67–√3

Answer 1

To find out which expression simplifies to $87-\sqrt{3}$, we can analyze each of the provided options one by one.

1. Option 1: $-67-\sqrt{3}-27-\sqrt{3}$ $$=-67-27-\sqrt{3}-\sqrt{3}=-94-2\sqrt{3}(\text{not }87-\sqrt{3})$$

2. Option 2: $-6\sqrt[3]{7}-2\sqrt[3]{7}$ $$=-8\sqrt[3]{7}(\text{clearly not }87-\sqrt{3})$$

3. Option 3: $36-\sqrt{3}+51-\sqrt{3}$ $$=(36+51)-(1\sqrt{3}+1\sqrt{3})=87-2\sqrt{3}(\text{not }87-\sqrt{3})$$

4. Option 4: $3\sqrt[3]{6}+5\sqrt[3]{1}$ $$=3\sqrt[3]{6}+5(\text{not }87-\sqrt{3})$$

5. Option 5: $256-\sqrt{3}-47-\sqrt{3}$ $$=(256-47)-(1\sqrt{3}+1\sqrt{3})=209-2\sqrt{3}(\text{not }87-\sqrt{3})$$

6. Option 6: $2\sqrt[3]{56}-4\sqrt[3]{7}$ $$=2\sqrt[3]{8\cdot 7}-4\sqrt[3]{7}=4\sqrt[3]{7}-4\sqrt[3]{7}=0(\text{not }87-\sqrt{3})$$

7. Option 7: $56-\sqrt{3}+67-\sqrt{3}$ $$=(56+67)-(1\sqrt{3}+1\sqrt{3})=123-2\sqrt{3}(\text{not }87-\sqrt{3})$$

None of the expressions provided simplifies to $87-\sqrt{3}$. Please double-check the expressions given or provide additional context.