Question

which integer is closest to $sqrt3{-9}$?

Explanation:

Step1: Identify nearby cube integers

We know that $(-2)^3 = -8$ and $(-3)^3 = -27$.

Step2: Calculate distance to each integer

Distance from $\sqrt[3]{-9}$ to $-2$: $|\sqrt[3]{-9} - (-2)| = |-\sqrt[3]{9} + 2| = 2 - \sqrt[3]{9} \approx 2 - 2.08 = 0.08$
Distance from $\sqrt[3]{-9}$ to $-3$: $|\sqrt[3]{-9} - (-3)| = |-\sqrt[3]{9} + 3| = 3 - \sqrt[3]{9} \approx 3 - 2.08 = 0.92$

Step3: Compare distances

0.08 is smaller than 0.92, so $\sqrt[3]{-9}$ is closer to $-2$.

Answer:

$-2$