Which expression simplifies to 87–√3

To find which expression simplifies to \( 87 - \sqrt{3} \), let's simplify each of the provided options one by one.

1. **Option 1: \( -67 - \sqrt{3} - 27 - \sqrt{3} \)**
Simplifying:
\[
-67 - 27 - \sqrt{3} - \sqrt{3} = -94 - 2\sqrt{3}
\]
This does not equal \( 87 - \sqrt{3} \).

2. **Option 2: \( -6\sqrt[3]{7} - 2\sqrt[3]{7} \)**
Simplifying:
\[
-6\sqrt[3]{7} - 2\sqrt[3]{7} = -8\sqrt[3]{7}
\]
This does not equal \( 87 - \sqrt{3} \).

3. **Option 3: \( 36 - \sqrt{3} + 51 - \sqrt{3} \)**
Simplifying:
\[
36 + 51 - \sqrt{3} - \sqrt{3} = 87 - 2\sqrt{3}
\]
This does not equal \( 87 - \sqrt{3} \).

4. **Option 4: \( 256 - \sqrt{3} - 47 - \sqrt{3} \)**
Simplifying:
\[
256 - 47 - \sqrt{3} - \sqrt{3} = 209 - 2\sqrt{3}
\]
This does not equal \( 87 - \sqrt{3} \).

5. **Option 5: \( 56 - \sqrt{3} + 67 - \sqrt{3} \)**
Simplifying:
\[
56 + 67 - \sqrt{3} - \sqrt{3} = 123 - 2\sqrt{3}
\]
This does not equal \( 87 - \sqrt{3} \).

None of the options given lead directly to \( 87 - \sqrt{3} \). Therefore, none of these expressions simplify to the required expression.

use the closest option

Given that we need to select the expression that is closest to \( 87 - \sqrt{3} \), let's examine the previously simplified options for their closeness:

1. **Option 1**: \( -94 - 2\sqrt{3} \)
2. **Option 2**: \( -8\sqrt[3]{7} \)
3. **Option 3**: \( 87 - 2\sqrt{3} \)
4. **Option 4**: \( 209 - 2\sqrt{3} \)
5. **Option 5**: \( 123 - 2\sqrt{3} \)

Among these options, **Option 3: \( 87 - 2\sqrt{3} \)** is the closest expression to \( 87 - \sqrt{3} \).

**Reason**:
The only difference is in the coefficient of \( \sqrt{3} \): \( 2\sqrt{3} \) vs. \( \sqrt{3} \). Since both expressions have the same constant term \( 87 \), Option 3 retains that value.

So, the closest option that simplifies to something approximating \( 87 - \sqrt{3} \) is:

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