Question

points k, l, m, and n are shown on the number line below.
number line image with k, l, m, n and -6 to 6
which point on the number line best approximates the location of $-2\sqrt{3}$?
a. point k
b. point l
c. point m
d. point n

Explanation:

Step1: Approximate $\sqrt{3}$

We know that $\sqrt{1} = 1$ and $\sqrt{4} = 2$, so $1<\sqrt{3}<2$. A better approximation: $\sqrt{3}\approx1.732$.

Step2: Calculate $-2\sqrt{3}$

Multiply $\sqrt{3}$ by $-2$: $-2\sqrt{3}\approx - 2\times1.732=-3.464$.

Step3: Analyze the number line points

• Point K: Around -5.
• Point L: Around -3.5 (since it's between -4 and -3, closer to -3.5).
• Point M: Around 3.5.
• Point N: Around 5.

The value $-3.464$ is closest to the location of point L.

Answer:

B. point L