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

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

56−−√3+67–√3

Answer 1

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.

Answer 2

use the closest option

Answer 3

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