What is −34–√3⋅216−−√3

Question

?(1 point)
Responses

48
48

−24
negative 24

−48
negative 48

24
24

Answer 1

To solve the expression $-34-\sqrt{3}\cdot 216-\sqrt{3}$, we first need to simplify it step by step.

1. Calculate $\sqrt{3}\cdot 216$: $$\sqrt{3}\cdot 216=216\sqrt{3}$$

2. Substitute back into the expression: $$-34-216\sqrt{3}-\sqrt{3}$$

3. Combine the $\sqrt{3}$ terms: $$-34-(216+1)\sqrt{3}=-34-217\sqrt{3}$$

However, we aren't looking for a numerical value since we didn't calculate the numerical approximation of $\sqrt{3}$.

We instead examine the structure. Since $-34$ and $-217\sqrt{3}$ are both negative terms, we see that the overall expression will also be negative.

As the prompt you provided lists only simplified numerical answers (48, -24, -48, 24), it suggests the full calculation might be overwhelmed by the negative terms.

Since $\sqrt{3}$ is about 1.732, we can estimate $217\sqrt{3}$: $$217\sqrt{3}\approx 217\cdot 1.732\approx 376.924$$ This would yield an estimate around $-34-376.924$, which will be significantly negative.

The most feasible answer, based on the choices given, is $$\text{negative }48$$ because $-34-376.924$ would be a much larger negative value, closer to -400.

Thus, the answer is: −48