Question

1. the points on the number line represent the values of four different numbers. which point best represents the value of \\(\sqrt{3}\\)?

a point a
b point b
c point c
d point d
(there is a number line with 0, 1, 2, 3, 4 marked, and points a at 1, b between 1 and 2, c between b and 2, d at 3)

Explanation:

Step1: Identify nearby perfect squares

We know that $1^2=1$ and $2^2=4$, so $\sqrt{1}=1$ and $\sqrt{4}=2$.

Step2: Narrow down $\sqrt{3}$ range

Since $1<3<4$, we get $1<\sqrt{3}<2$. $\sqrt{3}\approx1.732$, which is closer to 2 than 1.

Step3: Match to number line points

Point A is at 1, Points B and C are between 1 and 2, with C closer to 2. Point D is at 3. $\sqrt{3}\approx1.732$ aligns with Point C.

Answer:

C Point C