To determine where [tex]\(\sqrt{24}\)[/tex] would be plotted on the number line, we start by identifying between which two consecutive integers [tex]\(\sqrt{24}\)[/tex] lies.
First, we approximate the value of [tex]\(\sqrt{24}\)[/tex]. We find that:
[tex]\[
\sqrt{24} \approx 4.898979485566356
\][/tex]
Next, we need to determine the two integers between which this value falls. Clearly, [tex]\(\sqrt{24}\)[/tex] is greater than 4 and less than 5, as [tex]\(4.898979485566356\)[/tex] lies between 4 and 5.
Now, to establish whether [tex]\(\sqrt{24}\)[/tex] is closer to 4 or to 5, we can compare it with the midpoint between 4 and 5. This midpoint is calculated as follows:
[tex]\[
\text{Midpoint} = \frac{4 + 5}{2} = 4.5
\][/tex]
Next, we compare the value of [tex]\(\sqrt{24}\)[/tex] with the midpoint:
[tex]\[
4.898979485566356 \, > \, 4.5
\][/tex]
Since [tex]\(4.898979485566356\)[/tex] is greater than 4.5, it means [tex]\(\sqrt{24}\)[/tex] is closer to 5 than to 4.
Therefore, [tex]\(\sqrt{24}\)[/tex] would be plotted on the number line:
Between 4 and 5, but closer to 5.
