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: \( -67 - \sqrt{3} - 27 - \sqrt{3} \) \[ = -67 - 27 - \sqrt{3} - \sqrt{3} = -94 - 2\sqrt{3} \quad (\text{not } 87 - \sqrt{3}) \]

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

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

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

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

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

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

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