Question

points k, l, m, and n are shown on the number line below.
which point on the number line best approximates the location of $-2\sqrt{3}$?
\bigcirc point k
\bigcirc point l
\bigcirc point m
\bigcirc 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 is $\sqrt{3}\approx1.732$.

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

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

Step3: Analyze the number line points

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

Since $-3.464$ is close to - 3.5, which matches the location of Point L.

Answer:

Point L