what is $sqrt{5}$?\nplace a dot on the number line at the best approximation.
what is $sqrt{5}$?\nplace a dot on the number line at the best approximation.
Answer
Explanation:
Step1: Identify nearby perfect squares
We know that $2^2=4$ and $3^2=9$, so $\sqrt{5}$ is between 2 and 3.
Step2: Calculate approximate value
$\sqrt{5} \approx 2.236$, so it is close to 2, about 0.24 units to the right of 2.
Step3: Locate on number line
The number line has 10 small ticks between each integer, so each tick represents 0.1. We move 2 small ticks to the right of 2 (since 0.2 is 2 ticks, and 0.236 is very close to this position).
Answer:
The best approximation of $\sqrt{5}$ is $\approx 2.24$, so the dot should be placed 2 small ticks to the right of the number 2 on the number line.