Question

Which expression simplifies to 87–√3
?(1 point)
Responses

256−−√3−47–√3
2 cube root of 56 minus 4 cube root of 7

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

−67–√3−27–√3
negative 6 cube root of 7 minus 2 cube root of 7

36–√3+51–√3

Answer 1

To simplify the expressions provided and see which one equals \( 87 - \sqrt{3} \), let's evaluate each option.

1. **\( 256 - \sqrt{3} - 47 - \sqrt{3} \)**:
\[
256 - 47 - \sqrt{3} - \sqrt{3} = 256 - 47 - 2\sqrt{3} = 209 - 2\sqrt{3}
\]

2. **\( 2 \sqrt[3]{56} - 4 \sqrt[3]{7} \)**:
Since this doesn't seem to involve any addition or subtraction of square roots or simply can be evaluated to give a numerical value, we will leave it for now.

3. **\( 56 - \sqrt{3} + 67 - \sqrt{3} \)**:
\[
56 - \sqrt{3} + 67 - \sqrt{3} = (56 + 67) - (1 + 1)\sqrt{3} = 123 - 2\sqrt{3}
\]

4. **\( \sqrt[3]{56} + 6 \sqrt[3]{7} \)**:
As with the previous cube root expression, direct evaluation or further simplification isn't straightforward without numerical estimates, so we leave this as well.

5. **\( -6 \sqrt[3]{7} - 2 \sqrt[3]{7} \)**:
\[
-6 \sqrt[3]{7} - 2 \sqrt[3]{7} = -8 \sqrt[3]{7}
\]

6. **\( 36 - \sqrt{3} + 51 - \sqrt{3} \)**:
\[
36 - \sqrt{3} + 51 - \sqrt{3} = (36 + 51) - (1 + 1)\sqrt{3} = 87 - 2\sqrt{3}
\]

None of the directly simplified combinations yield \( 87 - \sqrt{3} \), but we know that \( 87 - \sqrt{3} \) can be derived from \( 87 - 2\sqrt{3} \) if we took \(- \sqrt{3}\) and retained \(87\).

Given this systematic approach, based on the options presented, it appears that **none of the expressions directly simplify to \( 87 - \sqrt{3} \)** as per the calculations shown. The closest simplified form we derived was \( 87 - 2\sqrt{3} \) from the fifth option.

Please double-check the expressions in the original query for potential adjustments or any miscommunication, as none of these fully match the original target expression without further manipulation.