Which expression simplifies to 87–√3

Question

?(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

56−−√3+67–√3
cube root of 56 plus 6 cube root of 7

256−−√3−47–√3

Answer 1

To determine which expression simplifies to \(87 - \sqrt{3}\), we will simplify each of the provided expressions one by one.

1. Expression: \( -67 - \sqrt{3} - 27 - \sqrt{3} \)

   • Combine the constants: \(-67 - 27 = -94\)
   • Combine the square roots: \(-\sqrt{3} - \sqrt{3} = -2\sqrt{3}\)
   • Result: \(-94 - 2\sqrt{3}\) (Not equal to \(87 - \sqrt{3}\))

2. Expression: \( -6 \sqrt[3]{7} - 2 \sqrt[3]{7} \)

   • Combine like terms: \(-6\sqrt[3]{7} - 2\sqrt[3]{7} = -8\sqrt[3]{7}\)
   • Result: \(-8\sqrt[3]{7}\) (Not equal to \(87 - \sqrt{3}\))

3. Expression: \( 36 - \sqrt{3} + 51 - \sqrt{3} \)

   • Combine the constants: \(36 + 51 = 87\)
   • Combine the square roots: \(-\sqrt{3} - \sqrt{3} = -2\sqrt{3}\)
   • Result: \(87 - 2\sqrt{3}\) (Not equal to \(87 - \sqrt{3}\))

4. Expression: \( \sqrt[3]{56} + 6 \sqrt[3]{7} \)

   • This does not contain any square root terms and doesn't simplify to \(87 - \sqrt{3}\).
   • Result: \(\sqrt[3]{56} + 6\sqrt[3]{7}\) (Not equal to \(87 - \sqrt{3}\))

5. Expression: \( 256 - \sqrt{3} - 47 - \sqrt{3} \)

   • Combine the constants: \(256 - 47 = 209\)
   • Combine the square roots: \(-\sqrt{3} - \sqrt{3} = -2\sqrt{3}\)
   • Result: \(209 - 2\sqrt{3}\) (Not equal to \(87 - \sqrt{3}\))

None of the options provided simplifies to \(87 - \sqrt{3}\). Therefore, the answer is none of the above.