The problem asks us to identify which point on the number line (m, n, or o) most closely represents $-\sqrt{84}$.

1. Problem Description

The problem asks us to identify which point on the number line (m, n, or o) most closely represents $-\sqrt{84}$.

2. Solution Steps

First, we need to find the value of $\sqrt{84}$.

Since $9^2 = 81$ and $10^2 = 100$, we know that $\sqrt{84}$ is between 9 and

1

0.

We can approximate $\sqrt{84}$ using a calculator, which gives $\sqrt{84} \approx 9.165$.

Therefore, $-\sqrt{84} \approx -9.165$.

Looking at the number line, the points are:

m is around -9.2

n is between -9.2 and -9.1

o is around -9.1

Since $-9.165$ is between -9.2 and -9.1, and closer to -9.2, the point that most closely represents $-\sqrt{84}$ is point 'n'.

3. Final Answer

n